The generator matrix

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

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+248x^37+418x^38+880x^39+1079x^40+1312x^41+1532x^42+1880x^43+1717x^44+1954x^45+1559x^46+1438x^47+878x^48+692x^49+369x^50+244x^51+99x^52+50x^53+23x^54+6x^55+2x^56+3x^58

The gray image is a linear code over GF(2) with n=176, k=14 and d=74.
This code was found by Heurico 1.13 in 6.58 seconds.