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  1  1  1  1  1  X  1  1  0  1  0  1 X^2  1  1  1  0  X  1  X  1 X^2  1 X^2  X  X  1  1  1 X^2  1  1  1  X X^2  1  1  1  0  X  X  X  1 X^2  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X X^2+X X^2+X X^2  0  0 X^2+X X^2  0 X^2  X  X X^2+X X^2 X^2+X  X X^2+X X^2 X^2  0  X  X  X X^2  X X^2  X X^2 X^2+X X^2 X^2 X^2  0  X X^2 X^2  X  0 X^2  0  X  X X^2  X X^2+X  X  X  X X^2 X^2+X X^2  X X^2+X  X X^2+X  0  X X^2  X  X  X X^2  X X^2+X X^2+X  X  0  X X^2+X
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X X^2  0 X^2+X X^2+X X^2 X^2+X X^2 X^2+X  0 X^2 X^2 X^2+X X^2+X  0 X^2+X  0 X^2  0 X^2+X X^2+X X^2+X X^2  0  X  0  0  0 X^2 X^2 X^2+X  X  X  X X^2  0 X^2  0 X^2  X X^2 X^2+X  X X^2+X  0  X X^2+X X^2  X  0  0  X  0 X^2 X^2+X X^2 X^2+X X^2+X  0 X^2 X^2+X X^2 X^2  X X^2+X  0 X^2+X X^2+X X^2
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2+X  0  X X^2  X  X  0 X^2  X  0 X^2+X  X  X X^2+X X^2 X^2+X  0  0  X  X  0  X X^2 X^2+X X^2  0 X^2+X X^2 X^2+X X^2 X^2+X  0 X^2+X  X  X X^2+X X^2+X X^2+X X^2  0  0 X^2 X^2  X  0  0  X  X  0  X  0 X^2+X  0  0 X^2+X  X X^2  X  0  X X^2  X  0  0  X X^2  0 X^2
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  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  0 X^2  0 X^2 X^2  0  0 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+117x^76+342x^78+451x^80+521x^82+797x^84+587x^86+491x^88+287x^90+220x^92+141x^94+74x^96+32x^98+20x^100+6x^102+2x^104+4x^106+2x^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 2.05 seconds.