The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1  0  1  1 X^2  X  1  1  X  1  1 X^2  1  1  1  1  1 X^2 X^2  1  1  X  1  1  1 X^2  1  1  1  1  1  1  0 X^2+X  1 X^2+X  1 X^2 X^2+X  0  1 X^2  X  X  X X^2  X  0  X  0  X  X X^2+X X^2+X X^2  X  0  1 X^2 X^2  1  1  1  1  1  1 X^2  X  1  1  0
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X  1 X^2+1  X X+1  1 X^2 X^2+1  1  1 X^2+X  1  1  0 X^2+X+1  1  1 X^2+X  0 X^2+X+1 X^2+X+1  1  1 X^2 X^2+X  1  1 X^2+X X+1  1 X^2+X X^2+X+1 X^2 X^2+X X+1  1  1  1 X^2+X  1 X+1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1 X^2+X+1  1  1  0 X^2+1 X^2+X X^2+1 X^2+X+1  0  1  X  0 X+1  1
 0  0  X  0 X^2+X  0 X^2+X X^2  X  X  X X^2 X^2+X  0 X^2 X^2+X X^2 X^2+X  X  0 X^2+X X^2  0  X  0  X  0 X^2  0 X^2+X X^2+X X^2 X^2+X X^2  X X^2+X  X X^2 X^2+X X^2  0  X  X  X X^2  0 X^2 X^2 X^2+X  0 X^2  0 X^2  0  X  X  0  0 X^2+X X^2+X  X  0  X  X X^2  X X^2  0  0 X^2 X^2  0 X^2  X X^2  X X^2  X X^2+X  0  0  X  X  0
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+54x^76+88x^77+326x^78+168x^79+472x^80+120x^81+510x^82+136x^83+472x^84+136x^85+514x^86+120x^87+379x^88+168x^89+196x^90+88x^91+62x^92+30x^94+15x^96+22x^98+10x^100+2x^102+3x^104+2x^108+2x^120

The gray image is a linear code over GF(2) with n=336, k=12 and d=152.
This code was found by Heurico 1.16 in 1.59 seconds.