The generator matrix

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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+34x^76+100x^77+145x^78+328x^79+288x^80+634x^81+402x^82+710x^83+473x^84+794x^85+496x^86+900x^87+458x^88+692x^89+358x^90+514x^91+199x^92+286x^93+99x^94+86x^95+56x^96+40x^97+18x^98+16x^99+19x^100+12x^101+11x^102+6x^103+4x^104+2x^105+6x^106+3x^108+1x^112+1x^118

The gray image is a linear code over GF(2) with n=344, k=13 and d=152.
This code was found by Heurico 1.16 in 6.19 seconds.