The generator matrix

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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+48x^34+140x^36+16x^37+225x^38+96x^39+425x^40+240x^41+715x^42+320x^43+711x^44+240x^45+422x^46+96x^47+203x^48+16x^49+98x^50+43x^52+25x^54+11x^56+3x^58+1x^60+1x^68

The gray image is a linear code over GF(2) with n=172, k=12 and d=68.
This code was found by Heurico 1.16 in 0.834 seconds.