The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  0  X  1  1  X  1 X^2+X  X  1  1  1  X  1  1  X  1  X  0 X^2+X  1  1 X^2+X  0 X^2+X  X X^2  X  1  1  1  1  0  1  1  1
 0  1  0  0  1 X+1  1 X^2+X X^2+1  1  X X^2+1 X^2+X  1 X^2+X+1  1  1  1 X^2+X  0  X X^2+X+1  0  1 X+1 X^2+X X^2  1  0 X^2+X  1  1  0  1  1  1  X  1 X^2+1 X^2+X+1  1  0 X^2 X^2
 0  0  1  1  1  0  1 X^2+1  1  1  1  0 X^2  X  1  X  1 X^2 X+1 X^2  1 X+1  X X^2+X X^2  1  1 X^2+X+1 X^2+X X^2+X+1 X^2+X+1  1  1 X^2 X^2+X+1 X^2  0 X+1 X^2+X+1 X^2+X X^2+X  0  0 X^2
 0  0  0  X  0  0 X^2 X^2 X^2+X  X  X X^2+X  X X^2+X X^2+X  X X^2  X  X X^2+X X^2+X X^2 X^2  0 X^2 X^2  0 X^2+X X^2 X^2 X^2+X X^2 X^2+X  0  X X^2  0  X  0  X  0 X^2+X X^2 X^2+X
 0  0  0  0  X X^2  X X^2+X X^2 X^2 X^2+X  X  X X^2+X X^2+X  0 X^2 X^2 X^2+X X^2 X^2  0  X X^2+X X^2+X  0 X^2+X X^2+X  0 X^2  0 X^2+X  X  0  0  0 X^2+X  X X^2+X  0  0 X^2+X X^2+X  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+68x^37+210x^38+418x^39+606x^40+664x^41+805x^42+942x^43+908x^44+884x^45+830x^46+700x^47+480x^48+274x^49+179x^50+96x^51+50x^52+44x^53+22x^54+2x^55+3x^56+2x^57+2x^58+2x^59

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 2.08 seconds.