The generator matrix

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

generates a code of length 88 over Z2[X]/(X^4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+166x^81+875x^82+1694x^83+2291x^84+2986x^85+3297x^86+3618x^87+3609x^88+3626x^89+3248x^90+2618x^91+1948x^92+1190x^93+716x^94+458x^95+173x^96+112x^97+58x^98+12x^99+25x^100+28x^101+5x^102+5x^104+4x^105+1x^106+4x^108

The gray image is a linear code over GF(2) with n=704, k=15 and d=324.
This code was found by Heurico 1.16 in 18.5 seconds.