The generator matrix

 1  0  0  1  1  1  X  1  1 X^2+X  1 X^2  1  1 X^2 X^2+X  1  X  1  1  1  1  X X^2+X  0  1 X^2+X  1  1  1  1  1 X^2  0  0  1  1  1 X^2  0  1  1  0  1
 0  1  0  X  1 X^2+X+1  1 X^2+X  0 X^2  1  1 X^2+X X^2+1  1  1 X+1  1 X^2+1 X^2+X+1 X^2  X X^2+X  1  1 X^2+X  1 X^2 X^2+1  0 X^2  1  1  1  0 X^2+X X^2+X+1  1  0  1 X^2+X  X X^2  0
 0  0  1  1 X^2+X+1 X^2+X  1 X+1 X^2+X  1  1  1  0  0  X X+1 X+1 X^2+X  1 X^2  1 X^2+X  1  0 X+1 X^2 X^2+X+1  1  0 X+1  0 X^2 X^2  X  1 X^2+X X^2+1 X+1  1  X  X X+1  1 X^2
 0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 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  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0  0 X^2  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 X^2  0 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 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  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 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  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+64x^37+279x^38+360x^39+584x^40+634x^41+901x^42+740x^43+1125x^44+794x^45+910x^46+602x^47+523x^48+270x^49+202x^50+82x^51+64x^52+30x^53+11x^54+6x^55+4x^56+1x^58+2x^59+3x^60

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 2.21 seconds.