The generator matrix

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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+178x^85+961x^86+1158x^87+1778x^88+1838x^89+2192x^90+1498x^91+1772x^92+1306x^93+1297x^94+868x^95+636x^96+258x^97+298x^98+122x^99+105x^100+44x^101+44x^102+18x^103+1x^104+8x^105+3x^108

The gray image is a linear code over GF(2) with n=728, k=14 and d=340.
This code was found by Heurico 1.16 in 11.5 seconds.