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

generates a code of length 84 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+62x^75+125x^76+156x^77+201x^78+192x^79+269x^80+282x^81+322x^82+384x^83+369x^84+372x^85+235x^86+268x^87+190x^88+132x^89+144x^90+56x^91+99x^92+60x^93+43x^94+42x^95+27x^96+18x^97+14x^98+18x^99+7x^100+4x^101+1x^102+2x^103+1x^128

The gray image is a linear code over GF(2) with n=336, k=12 and d=150.
This code was found by Heurico 1.16 in 32.3 seconds.