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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+39x^66+46x^67+120x^68+128x^69+159x^70+194x^71+229x^72+304x^73+352x^74+400x^75+365x^76+344x^77+297x^78+282x^79+187x^80+174x^81+118x^82+84x^83+74x^84+62x^85+34x^86+12x^87+39x^88+10x^89+18x^90+6x^91+9x^92+2x^93+5x^94+1x^102+1x^114

The gray image is a linear code over GF(2) with n=304, k=12 and d=132.
This code was found by Heurico 1.16 in 1.76 seconds.