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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  X  X  X  1  X  X  X  X  X  X  X  X  X
 0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2
 0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0
 0  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+30x^85+6x^86+64x^87+9x^88+9x^90+6x^92+1x^114+2x^117

The gray image is a linear code over GF(2) with n=348, k=7 and d=170.
This code was found by Heurico 1.16 in 1.51 seconds.