The generator matrix

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

generates a code of length 88 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+168x^84+718x^85+686x^86+608x^87+488x^88+418x^89+222x^90+164x^91+180x^92+172x^93+104x^94+80x^95+34x^96+48x^97+2x^98+1x^102+1x^106+1x^108

The gray image is a linear code over GF(2) with n=704, k=12 and d=336.
This code was found by Heurico 1.16 in 11.9 seconds.