The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+72x^35+274x^36+430x^37+844x^38+1374x^39+1821x^40+2458x^41+3209x^42+3876x^43+4068x^44+3774x^45+3204x^46+2760x^47+1975x^48+1078x^49+686x^50+404x^51+234x^52+124x^53+56x^54+26x^55+11x^56+8x^57+1x^58

The gray image is a linear code over GF(2) with n=176, k=15 and d=70.
This code was found by Heurico 1.16 in 26.9 seconds.