The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  1  1  X  1  1  1  1  1  X  1  X  1  1  X  1  0 X^2  1  1  X  X  X  1  X
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X  0 X^2+X X^3 X^2+X X^3+X X^2 X^2  X  0 X^2+X X^2 X^3+X X^3 X^3+X X^3 X^3+X X^2+X  0 X^3+X X^2  X X^3 X^2+X  0 X^2  X  0 X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X  0  0 X^3+X^2+X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^2+X X^3+X^2 X^2 X^3+X X^3+X^2  X X^3 X^3+X^2+X X^2+X  0 X^3+X X^3+X^2 X^2 X^3+X^2 X^2+X X^3+X^2+X X^2+X X^3+X^2  X X^3+X^2 X^2+X X^3+X^2  X X^3+X^2+X X^3 X^2  X X^2 X^3+X X^2+X X^2+X X^3+X^2+X X^3 X^2+X
 0  0 X^3+X^2  0 X^2  0 X^3  0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2  0  0  0 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3  0  0 X^3+X^2 X^3+X^2  0 X^2 X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3 X^3 X^3  0 X^3 X^3 X^2 X^3 X^3+X^2 X^3 X^2 X^3  0 X^3 X^3+X^2 X^2 X^3  0 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3
 0  0  0 X^3+X^2  0 X^3 X^3 X^2 X^2 X^2 X^2  0  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3  0 X^3 X^3 X^2 X^3+X^2 X^3+X^2  0 X^3 X^3  0 X^3+X^2  0 X^3  0 X^2 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3  0 X^3 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2  0 X^3+X^2 X^3 X^3
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3

generates a code of length 81 over Z2[X]/(X^4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+136x^75+160x^76+256x^77+209x^78+402x^79+539x^80+790x^81+557x^82+372x^83+208x^84+196x^85+47x^86+74x^87+44x^88+62x^89+18x^90+8x^91+4x^92+8x^93+4x^96+1x^138

The gray image is a linear code over GF(2) with n=648, k=12 and d=300.
This code was found by Heurico 1.16 in 72.9 seconds.