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

generates a code of length 88 over Z2[X]/(X^4) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+146x^85+70x^86+300x^87+124x^88+176x^89+48x^90+84x^91+2x^92+62x^93+8x^94+1x^104+1x^106+1x^130

The gray image is a linear code over GF(2) with n=704, k=10 and d=340.
This code was found by Heurico 1.16 in 1.08 seconds.