The generator matrix

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

generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+30x^84+168x^85+292x^86+48x^87+282x^88+168x^89+26x^90+6x^92+1x^96+1x^106+1x^138

The gray image is a linear code over GF(2) with n=696, k=10 and d=336.
This code was found by Heurico 1.16 in 0.469 seconds.