The generator matrix

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

generates a code of length 89 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+122x^87+224x^88+388x^89+166x^90+74x^91+22x^92+24x^93+1x^108+1x^110+1x^130

The gray image is a linear code over GF(2) with n=712, k=10 and d=348.
This code was found by Heurico 1.16 in 1.94 seconds.