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  X  0  X X^3+X^2  X  0  X X^3+X^2  X  0  X X^3+X^2  X  0  X X^3  X  X X^3+X^2 X^2  X  X X^2  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X X^3+X^2  0 X^2+X X^3+X^2  X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2  X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2 X^3+X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2 X^3+X X^3 X^3+X^2+X X^2 X^3+X X^2+X  0  X X^2 X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2  X X^2+X  X X^3+X  X X^2+X  X X^3+X  X X^2+X  X X^3+X  X X^2+X  X X^3+X^2+X  X X^3+X  X  X  X  0  0  0  0
 0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0  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+34x^84+154x^85+58x^86+208x^87+28x^88+356x^89+4x^90+160x^91+18x^93+1x^104+1x^106+1x^130

The gray image is a linear code over GF(2) with n=704, k=10 and d=336.
This code was found by Heurico 1.16 in 0.813 seconds.