The generator matrix

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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+276x^86+224x^87+528x^88+240x^89+583x^90+608x^91+459x^92+256x^93+382x^94+192x^95+206x^96+16x^97+101x^98+20x^100+1x^102+1x^124+1x^126+1x^128

The gray image is a linear code over GF(2) with n=728, k=12 and d=344.
This code was found by Heurico 1.16 in 1 seconds.