The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+192x^74+140x^75+393x^76+228x^77+364x^78+228x^79+418x^80+336x^81+362x^82+276x^83+345x^84+196x^85+258x^86+92x^87+108x^88+40x^89+46x^90+24x^92+18x^94+12x^96+8x^98+8x^100+1x^104+2x^108

The gray image is a linear code over GF(2) with n=324, k=12 and d=148.
This code was found by Heurico 1.16 in 2.99 seconds.