The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  0  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  1  0  1  1 X^2+X  0  1  1  1  1  1 X^2+X X^2+X X^2+X  1  1  X  1  1  X
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  1  0 X^2+1  1 X^2+X X+1  1 X+1  0  1 X^2+1 X^2+X X^2+1  1 X+1  0  1  1 X^2+X X+1  0 X^2+X X^2+1  1  1  1 X^2+1 X^2+1  0 X^2+1 X^2+X  1
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 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 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0  0  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  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2
 0  0  0  0  0  0 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 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  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 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0  0 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+140x^36+48x^37+204x^38+208x^39+648x^40+496x^41+936x^42+784x^43+1285x^44+784x^45+976x^46+496x^47+597x^48+208x^49+184x^50+48x^51+102x^52+4x^54+34x^56+9x^60

The gray image is a linear code over GF(2) with n=176, k=13 and d=72.
This code was found by Heurico 1.16 in 2.46 seconds.