The generator matrix

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

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+130x^38+32x^39+232x^40+56x^41+272x^42+176x^43+341x^44+128x^45+261x^46+112x^47+140x^48+8x^49+81x^50+46x^52+21x^54+7x^56+3x^58+1x^68

The gray image is a linear code over GF(2) with n=176, k=11 and d=76.
This code was found by Heurico 1.16 in 0.28 seconds.