The generator matrix

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

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+62x^39+182x^40+204x^41+319x^42+220x^43+300x^44+202x^45+143x^46+92x^47+113x^48+84x^49+69x^50+24x^51+8x^52+6x^53+13x^54+2x^55+2x^56+2x^64

The gray image is a linear code over GF(2) with n=176, k=11 and d=78.
This code was found by Heurico 1.11 in 0.063 seconds.