The generator matrix

 1  0  0  0  0  0  0  1  1  1  0  1  X  1  1  0  1  0  X  X  1  1  1  X  1  0  1  1  0  1  1  0  1  0  1  1  1  1  1  X  1  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  X  0  X  X  1  1  1  1  1  1 X+1  1  1  1  1  1  0 X+1  1  1  1  X  1  1  X
 0  0  1  0  0  0  0  0  0  0  0  0  0  X  0  0  X  1  1  1 X+1 X+1 X+1 X+1  1  0  X  0  X  1  1  1  X X+1 X+1  1  1  0  1  1  1  X  1  1
 0  0  0  1  0  0  0  0  0  X  X  1  1 X+1 X+1  1  1  0  0 X+1 X+1  0 X+1  X  0 X+1  1  X X+1 X+1 X+1  0  X  1  0  1  0  X  X  X  0 X+1  0  0
 0  0  0  0  1  0  0  X  1 X+1  1  0  1  1  1 X+1  X  1  1  1  X  0  1  0  0  X  1  0 X+1  0  1 X+1 X+1  X  0  0  1 X+1  1  X  0  0 X+1  0
 0  0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  0  X X+1 X+1  X X+1  X X+1  1  0  0  1  X  X  1 X+1  1 X+1  1  X  0 X+1  X  X  1  1  1  1  1  0
 0  0  0  0  0  0  1  1  X  1  1 X+1  X  1  X  1  X  1 X+1  X X+1 X+1 X+1 X+1  X  X X+1  1  1  X  X  0 X+1 X+1  1  1  X  X  1  1 X+1  1  0  0

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+68x^33+221x^34+290x^35+370x^36+522x^37+696x^38+798x^39+910x^40+1116x^41+1177x^42+1308x^43+1269x^44+1296x^45+1336x^46+1164x^47+1021x^48+820x^49+671x^50+442x^51+366x^52+242x^53+112x^54+86x^55+28x^56+28x^57+11x^58+8x^59+2x^60+4x^61+1x^76

The gray image is a linear code over GF(2) with n=88, k=14 and d=33.
This code was found by Heurico 1.16 in 40.7 seconds.