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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+298x^84+224x^85+528x^86+240x^87+506x^88+608x^89+488x^90+256x^91+411x^92+192x^93+224x^94+16x^95+91x^96+8x^98+2x^100+2x^120+1x^124

The gray image is a linear code over GF(2) with n=712, k=12 and d=336.
This code was found by Heurico 1.16 in 0.797 seconds.