The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+338x^38+224x^39+911x^40+386x^41+1209x^42+472x^43+1327x^44+402x^45+1174x^46+346x^47+760x^48+134x^49+338x^50+70x^51+73x^52+6x^53+12x^54+6x^55+1x^58+2x^59

The gray image is a linear code over GF(2) with n=176, k=13 and d=76.
This code was found by Heurico 1.16 in 2.41 seconds.