The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  X  1  1 X^2  1  1  1  X  1  X  1  1  1 X^2+X  1 X^2+X X^2 X^2 X^2  1  1  1  1  X  X  1  X X^2+X  1  1  1  1  1 X^2  1
 0  1  1 X^2+X X^2+X+1  1 X^2 X+1  1  1  X X^2+1  1  1  0 X^2+X+1  1 X^2  1 X+1 X^2 X^2+X  1 X^2+X+1  1  1  1  1 X^2+X+1 X^2+1 X^2+X X^2+X+1  1  1  0  1  1 X^2+1  1 X^2+1  0  0  X  0
 0  0  X  0 X^2+X  0  X X^2 X^2+X X^2+X  X X^2  X  X  0  X X^2 X^2+X X^2+X X^2 X^2  0  0  X  0  X  0 X^2+X  0 X^2  0 X^2  X  0  0 X^2+X  X X^2  0 X^2 X^2+X  X X^2+X  0
 0  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0
 0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 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+31x^38+144x^39+80x^40+320x^41+101x^42+302x^43+117x^44+352x^45+100x^46+270x^47+37x^48+120x^49+14x^50+18x^51+12x^52+8x^53+9x^54+2x^55+6x^56+1x^58+3x^60

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 0.166 seconds.