The generator matrix

 1  0  1  1  1 X^2+X X^2  1  1  1  1  0  0  1  1  1  X  1  1  0  1  0  1  X  1  1  1  1  1  X  1  1 X^2 X^2+X  1  1 X^2  1  1  1  X  X X^2  1  1  1 X^2+X  1  0  1  1 X^2  1  1 X^2+X  1  0  1  0  1  1  1  0  1  1  X  1 X^2  1 X^2  1  1  1  1  1 X^2+X X^2+X  0  1 X^2+X  X  1  0  1 X^2
 0  1  1  0  1  1  1  0 X+1 X^2 X+1  1  1 X^2+X+1 X^2  1  1  0  0  1 X^2+X+1  1 X^2+X  1 X+1  X  1 X^2+X X^2+1  1 X+1 X^2+X  1  1 X^2+X+1  X  1 X+1 X^2+X+1 X^2  1  1  1  0  X  1  1 X^2  1 X^2+X+1 X^2+X  1 X^2+1  0  1 X^2+X+1  1 X^2+X+1  1 X+1  X X+1  1 X+1 X^2+X+1  1 X^2+X+1  1 X^2  1 X^2+1  1 X^2 X^2 X^2+1  1  1  1  0  1 X^2+X X^2+1  X X^2+X+1  1
 0  0  X  0  0  0  0 X^2+X X^2  X X^2+X X^2+X  0  0 X^2 X^2  0 X^2 X^2+X X^2+X  X X^2+X X^2+X  X  X  X X^2 X^2  X X^2+X  X  0  X X^2+X X^2+X X^2 X^2+X  0  0 X^2+X X^2 X^2 X^2+X X^2+X  X  0  X X^2  0 X^2+X X^2 X^2+X X^2+X X^2+X  0  X  0 X^2  0  X X^2 X^2+X  X  0  X X^2+X  0  X  X X^2+X X^2+X X^2 X^2+X  X  X  X X^2+X X^2 X^2+X X^2+X X^2  X  X  0 X^2
 0  0  0  X  0  0  0  0 X^2+X  X  X X^2+X X^2+X  X  0 X^2  X X^2+X X^2  0  X X^2 X^2+X X^2+X X^2 X^2+X  X X^2+X X^2+X X^2 X^2+X X^2+X  X X^2  0 X^2  X X^2  X  0 X^2 X^2+X X^2  0 X^2  X X^2  0 X^2+X X^2+X  0  X  X X^2+X X^2+X  X X^2  0 X^2  0 X^2 X^2+X X^2+X X^2+X X^2  X  0  0  X X^2 X^2+X X^2 X^2+X X^2  0  X X^2  0 X^2  X  0 X^2  0 X^2  X
 0  0  0  0  X  0 X^2+X  X X^2+X X^2+X X^2  0 X^2+X  0  X  0 X^2  X X^2 X^2+X X^2+X  0 X^2  X  X X^2+X X^2  0  X  0 X^2  X X^2  X X^2  X  X  X X^2+X X^2 X^2+X  X  X  X X^2+X X^2  0 X^2 X^2  0  X  0 X^2  0  X X^2 X^2  X X^2+X X^2+X  0 X^2+X  0  0  0  0 X^2 X^2+X  0 X^2  X X^2+X X^2+X  0  0 X^2+X X^2 X^2+X X^2  0 X^2+X X^2+X  X X^2+X X^2+X
 0  0  0  0  0 X^2  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 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2  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  0 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+134x^76+92x^77+389x^78+240x^79+625x^80+420x^81+715x^82+492x^83+872x^84+544x^85+722x^86+560x^87+666x^88+404x^89+411x^90+236x^91+283x^92+76x^93+141x^94+8x^95+74x^96+41x^98+22x^100+12x^102+9x^104+1x^106+1x^108+1x^120

The gray image is a linear code over GF(2) with n=340, k=13 and d=152.
This code was found by Heurico 1.16 in 6.36 seconds.