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

generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+60x^64+64x^66+4x^67+267x^68+32x^69+256x^70+112x^71+470x^72+224x^73+436x^74+280x^75+508x^76+224x^77+356x^78+112x^79+317x^80+32x^81+156x^82+4x^83+116x^84+12x^86+24x^88+18x^92+8x^96+2x^100+1x^116

The gray image is a linear code over GF(2) with n=300, k=12 and d=128.
This code was found by Heurico 1.16 in 1.92 seconds.