The generator matrix

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

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+46x^37+109x^38+162x^39+276x^40+352x^41+429x^42+494x^43+481x^44+460x^45+382x^46+328x^47+234x^48+144x^49+90x^50+32x^51+30x^52+22x^53+13x^54+6x^55+1x^58+2x^59+1x^60+1x^64

The gray image is a linear code over GF(2) with n=176, k=12 and d=74.
This code was found by Heurico 1.16 in 0.888 seconds.