The generator matrix

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

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+186x^84+156x^86+384x^87+606x^88+384x^89+144x^90+177x^92+4x^94+5x^96+1x^172

The gray image is a linear code over GF(2) with n=704, k=11 and d=336.
This code was found by Heurico 1.16 in 8.78 seconds.