The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+276x^39+321x^40+470x^41+484x^42+402x^43+439x^44+382x^45+358x^46+334x^47+202x^48+222x^49+85x^50+58x^51+21x^52+30x^53+8x^54+2x^55+1x^58

The gray image is a linear code over GF(2) with n=176, k=12 and d=78.
This code was found by Heurico 1.16 in 64.6 seconds.