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 0 0 X 1 0 0 X X^2 1 1 X X^2 1 X^2 0 1 X^2 X 1 1
0 X 0 0 0 0 0 0 0 X X^2+X X X^2 X^2 X 0 X^2 X X^2+X X^2 X X^2+X 0 X X 0 X X X^2 X X^2+X 0 X^2 0 0 0 X X^2 X^2 X^2 X X^2+X 0 0
0 0 X 0 0 0 X X^2+X X X X 0 0 X X^2 X X^2 X X^2+X X^2 X^2+X 0 X^2 X^2 0 X^2 0 X X X^2 0 X X X^2 X^2+X X X^2 0 0 X^2 X X^2+X X 0
0 0 0 X 0 X X X X^2 0 0 X^2 X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X X X X 0 X X X X^2+X X^2 0 0 X^2 X X^2+X X^2+X X^2 X^2 X X X^2 X^2 0 X 0
0 0 0 0 X X X^2 X^2+X X^2+X 0 X X 0 X^2+X X X^2 X X X^2 X^2+X 0 0 0 X^2+X X^2+X X^2 0 X X^2 X^2+X X^2 0 X^2+X 0 X^2+X X^2+X X^2 X^2 X X^2+X X^2 X^2+X X^2+X 0
0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2
generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.
Homogenous weight enumerator: w(x)=1x^0+32x^36+92x^37+134x^38+268x^39+143x^40+480x^41+147x^42+698x^43+151x^44+746x^45+134x^46+478x^47+126x^48+174x^49+71x^50+86x^51+53x^52+42x^53+23x^54+6x^55+6x^56+2x^57+2x^58+1x^62
The gray image is a linear code over GF(2) with n=176, k=12 and d=72.
This code was found by Heurico 1.16 in 0.733 seconds.