The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+66x^37+240x^38+354x^39+617x^40+648x^41+956x^42+762x^43+1062x^44+756x^45+953x^46+574x^47+489x^48+296x^49+197x^50+94x^51+66x^52+26x^53+19x^54+8x^55+5x^56+3x^58

The gray image is a linear code over GF(2) with n=176, k=13 and d=74.
This code was found by Heurico 1.16 in 2.06 seconds.