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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+26x^80+78x^82+82x^84+128x^85+170x^86+128x^87+207x^88+102x^90+30x^92+30x^94+37x^96+4x^98+1x^168

The gray image is a linear code over GF(2) with n=348, k=10 and d=160.
This code was found by Heurico 1.16 in 0.596 seconds.