The generator matrix

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

generates a code of length 81 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+224x^75+352x^76+446x^77+320x^78+426x^79+346x^80+394x^81+284x^82+276x^83+167x^84+210x^85+108x^86+144x^87+122x^88+106x^89+44x^90+44x^91+32x^92+24x^93+12x^94+6x^95+3x^96+4x^97+1x^100

The gray image is a linear code over GF(2) with n=324, k=12 and d=150.
This code was found by Heurico 1.11 in 0.485 seconds.