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

generates a code of length 85 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+123x^76+8x^77+278x^78+56x^79+355x^80+128x^81+442x^82+176x^83+475x^84+248x^85+422x^86+248x^87+308x^88+112x^89+228x^90+32x^91+179x^92+16x^93+106x^94+67x^96+50x^98+23x^100+10x^102+4x^104+1x^128

The gray image is a linear code over GF(2) with n=340, k=12 and d=152.
This code was found by Heurico 1.16 in 2.02 seconds.