The generator matrix

 1  0  0  1  1  1  X X^3+X  1  1  1 X^3  1 X^3+X^2+X  1  1  1 X^3+X^2  0  1  X  1  1 X^3  1  1 X^3  1 X^3  1 X^2  1 X^2+X X^2+X  1  0  1  1  X  1 X^3+X^2+X X^2  1  1  1  1  0 X^3+X  1 X^3  1 X^2  1  1  X X^3+X  1  1  1  1  1  1  1  1  1  1 X^2 X^3  1  1 X^2  1  1 X^3+X  1  1  1  1 X^3+X  1  1  1  X  1  1  1  1  1  1
 0  1  0  0 X^2+1 X+1  1 X^3  0 X^3 X^3+X^2+1  1 X^2+X+1  1 X^3+X^2+X  0 X+1  1  1 X^2+1 X^2+X X^3+X^2 X^3+X+1  1  X  1  1  X X^2 X^3+X X^3+X^2+X  1  1  1 X^2+X+1  X X^3+X^2+X X^3+X+1  1  1 X^2  1  X X^3+X^2 X^3+X^2+1 X^2+X X^3 X^3+X^2  X  1 X^2+X+1  1 X^3+1 X^3+X^2  1  1  0 X^3+1 X^3+X^2+X X^2  0  X X^3+X+1 X^2+1  1  1  X  1  X X+1 X^3 X^3+X^2+1  0  1 X^3+X X^2+X X^2+1  0  1 X^3+X^2+1 X^2+X X^3+1 X^3+X^2  0 X^3+X^2+X X^2+X+1  1 X^2+X+1 X^2
 0  0  1  1  1  0 X^2+1  1  X X^3+X^2+X+1 X^3+X X^2+X+1  1 X^2+X X^3+1 X^2+X X^3+X^2 X^2 X+1 X+1  1 X^3+X^2+1 X^3+X+1  X X^3+X^2+1  X  1  0  1 X^2+X  1 X^3+X^2 X^3+X^2 X^3+X^2+1 X^2+X+1  1 X^2+X+1  X X^2+X X^3+X  1 X^2+X+1 X^2+X X^3+X+1 X^2+X+1  0  1  1 X^3+X  X X^3+1 X^3 X+1  0 X^3+1  1 X^3+X^2+1 X^3+X^2 X^3+X^2 X+1 X^2+1  0 X^2+X+1 X^3+1  1 X^3+X+1  1 X^2+1  1 X^3+X  1 X^2+1  X X^3 X^3  1  0 X^3+X+1 X^3+X+1 X^2 X^3+X^2+X X+1  1 X^3+X^2+1 X^3+X+1 X^3 X+1 X^2+X+1 X^2
 0  0  0  X X^3+X X^3 X^3+X X^3+X X^3+X  X  X X^3  0  X X^2+X X^3 X^3+X X^3+X X^3+X^2+X X^2+X X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3+X X^2+X X^3+X^2+X X^3+X^2+X X^3 X^3  X X^3+X^2 X^3+X X^2+X X^2+X  X X^2 X^2 X^2+X X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0  0 X^2+X X^2 X^3+X X^3+X X^3+X^2+X X^3 X^3+X^2+X  0 X^2+X X^3+X^2  X X^2+X  0  0  0 X^2+X X^3+X^2+X X^3+X^2 X^2 X^2 X^2  X  0 X^3+X^2+X X^3+X^2 X^3+X^2+X X^3+X X^2  X X^2+X X^3+X  X X^3  X X^2  0 X^3+X X^2 X^3+X^2  0

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+163x^82+976x^83+1465x^84+2402x^85+2801x^86+3394x^87+3945x^88+3816x^89+3362x^90+3304x^91+2368x^92+1772x^93+1203x^94+818x^95+431x^96+294x^97+82x^98+84x^99+26x^100+30x^101+4x^102+19x^104+6x^105+1x^106+1x^116

The gray image is a linear code over GF(2) with n=712, k=15 and d=328.
This code was found by Heurico 1.16 in 21.3 seconds.