The generator matrix

 1  0  1  1  1  X  1  1 X^2+X  1  1  X X^3+X^2+X X^2  1  1 X^3+X^2  1  1  1  1 X^3+X^2+X  1  1 X^3+X^2+X  1  1 X^2  1  1  1  1  1  0  1 X^3+X^2  1  1  X  1  1 X^3+X  1  1 X^3+X^2 X^3+X^2  1  1 X^2+X  1  1  0 X^3 X^3  0 X^3+X^2  X  0 X^3+X^2+X  1 X^3+X^2+X X^3 X^3+X X^3+X X^2 X^2+X X^2+X X^2  1 X^3+X  1  1  1 X^2+X  X  X  1 X^2+X X^3 X^3  1  1 X^3  1  1  1  1  1
 0  1  1 X^2 X+1  1  X X^3+1  1 X^2+X X^3+X+1  1  1  1  0 X^3+X^2+X+1  1 X^3+X^2 X^2+X+1 X^2+1 X^2+X  1 X^3+X X^3+X^2+1  1 X^2 X^3+1  1 X^3+1  0 X^3+X^2+X+1 X^3+X X^3+X^2+X+1  1 X^2+X  1 X^3+X^2+1 X^3+X^2  1 X^3+X^2+1  0  1 X^3+X^2+X  X  1  1 X^3+X+1 X^3+X+1  1 X^3+X+1 X^3+X  1  1  1  1  1 X^3  1  1 X^3+X^2+X  1  1  1  1  1  1  1  1 X^2  1 X^2+X+1 X^3+1 X^3+X^2  1  1  1 X^3+X^2+X+1  1  X  1 X^3+X^2+X+1 X^2+1  X X+1 X^2+X+1 X^3+1 X^2+X+1  0
 0  0  X X^3+X X^3 X^3+X X^3+X X^3  0  0  X X^2+X X^3+X^2 X^2 X^3+X^2 X^3+X^2+X X^2+X X^2+X X^2 X^3+X^2+X X^3+X^2 X^3+X X^2+X X^2 X^3+X^2+X X^2 X^2+X  X X^3+X^2 X^3+X^2+X  0 X^3 X^3+X X^2  X X^3+X^2+X X^3  0  0  X X^3+X X^2 X^3+X^2+X X^3+X^2  X  0 X^2 X^2+X X^3 X^3+X^2+X X^3+X^2+X X^2+X X^3+X^2+X  X X^3+X X^3 X^3+X^2+X X^3+X^2 X^2 X^2  X X^2 X^3+X^2+X X^3  0 X^3+X^2 X^3+X^2+X X^3+X^2 X^3+X^2  X  X X^2 X^3+X^2+X X^3+X X^2 X^3+X^2 X^3+X^2 X^2+X X^3+X^2 X^3+X X^2 X^3+X  X X^3+X X^3+X^2+X X^3+X^2+X X^2+X  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+53x^84+332x^85+309x^86+326x^87+194x^88+296x^89+160x^90+176x^91+77x^92+60x^93+34x^94+22x^95+2x^96+4x^99+1x^118+1x^128

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 1.78 seconds.