The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X^3+X  1  1  1  1 X^2 X^3+X^2+X  1  1 X^3  1  1 X^3+X  X  1  1  1  1 X^3+X  1 X^3  1  1  1 X^3+X  1  0  1  0  1  1  1 X^2+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^2+X  1 X^3+X^2  1 X^3+X^2+X  1  1  1  1  1 X^3+X X^2+X  1  1  1 X^3+X^2  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2 X^3+1  1 X+1 X^3+X^2+X  1  1  0 X^3+X^2+1 X^3 X^3+1  1  1 X^3+X X^2+X+1  1 X^3+X^2+X X^2+X+1  1  1 X^2 X^2+1 X^3+X^2  1  1 X^3+X  1 X^3+X+1 X^3+X^2+X X^2+1  1 X^2  1 X^3+X  1  0 X^3+X^2+X+1 X^3+X^2+1  1 X^2+1 X+1 X^3+X^2+1 X+1 X^3+X+1  0 X+1  X X^3+1 X^3+X^2+X+1 X^3+X^2+1 X^3+X^2+1 X^3+X^2+X+1 X^2+X+1 X+1 X^3+1  X X^2+X+1  1 X^2+X+1 X^3+1 X^2+X  1 X^2+1 X+1  1  1 X^2  1 X^2+X  1 X^3 X^3  1 X^3+X^2+X X^3+X^2+X+1  1  1 X^3+X^2 X^2+1  1  1 X^3+1  0
 0  0  X  0 X^3+X  X X^3+X X^3  0 X^3 X^3+X X^3+X^2+X X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2+X X^3+X^2 X^3+X^2+X X^3+X^2+X X^3+X X^3+X^2 X^3+X^2  0  X X^2 X^2+X X^2+X X^2 X^3+X^2+X X^3 X^2 X^2 X^3+X  X  X  0  0 X^2+X X^3+X^2 X^3+X X^3  0 X^3+X^2+X X^3 X^3+X  X X^3+X^2+X X^2  0  X X^2 X^3+X^2+X X^3 X^2 X^2+X X^3+X^2+X X^2+X X^3  X  0 X^3+X X^2 X^2 X^3 X^3+X^2 X^2+X  0 X^3+X^2+X  X X^3+X^2+X X^2+X X^2 X^3+X^2+X X^3 X^3+X^2 X^2+X  0 X^2  X  0  X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^2 X^2+X  0
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  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+121x^84+450x^85+329x^86+600x^87+352x^88+492x^89+345x^90+572x^91+270x^92+428x^93+70x^94+8x^95+15x^96+4x^97+11x^98+4x^99+8x^100+2x^101+12x^102+1x^126+1x^132

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 1.06 seconds.