The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1 X^3+X^2  1  1  X  1  1 X^3  1 X^2+X  1  1 X^2  1  1  1  0  1 X^3+X  1  1 X^3+X^2  1  1 X^2+X  1  1 X^3+X  1  1  1 X^2+X  1 X^3  1  1 X^3+X  1  1 X^2  1  X  X  1  1  0 X^3  1  1  1 X^3+X^2 X^3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3+X^2+X  1  1  0  1 X^3+X^2  1  1  1  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3 X^2+X+1  1 X^3+X^2 X^3+1  1  X X+1  1 X^3+X^2+1  1 X^2+X  1  1 X^2 X^3+X X^2+1  1 X^3+X^2+X+1  1 X^3 X^3+1  1 X^3+X^2+X X+1  1  X X^3+X^2+X+1  1 X^2 X^3+X^2+X X^3+X+1  1 X^3+X^2+1  1  X X^3+X^2+X+1  1 X^3+X^2  1  1  0  0 X^3+X  0 X^3+X^2+1  X  1  0 X^3+1 X^3+X^2+1  1  1 X^2 X^2 X^3 X^2 X^2+X X^2+X X^2+X  X X^3+X X^2+X X^3 X^2  X X^3+X X^3+X^2+X X^2+X X^3+X+1  1 X^3+X X^2+1  1 X^3+X^2  X  0 X^3+X^2+X+1 X^3+1  1 X^2+X+1  0
 0  0 X^2 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^2 X^3  0 X^3 X^3  0 X^3+X^2 X^3  0 X^3+X^2 X^3  0 X^2  0 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^2 X^2  0 X^2 X^3+X^2 X^3  0 X^3 X^2 X^3 X^3 X^3 X^2 X^3  0 X^3  0 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^2 X^3+X^2  0 X^2 X^3+X^2  0  0
 0  0  0 X^3  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  0  0  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0  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+104x^84+190x^85+436x^86+276x^87+265x^88+166x^89+254x^90+168x^91+78x^92+26x^93+74x^94+4x^95+2x^97+2x^110+1x^118+1x^126

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 0.843 seconds.