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

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+171x^76+264x^78+441x^80+584x^82+693x^84+612x^86+549x^88+316x^90+212x^92+116x^94+81x^96+28x^98+17x^100+7x^104+3x^108+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 2.23 seconds.