The generator matrix

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

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+80x^33+180x^34+266x^35+427x^36+540x^37+660x^38+830x^39+939x^40+1096x^41+1208x^42+1268x^43+1269x^44+1288x^45+1258x^46+1134x^47+1070x^48+854x^49+675x^50+516x^51+347x^52+210x^53+103x^54+76x^55+37x^56+26x^57+8x^58+6x^59+5x^60+2x^61+2x^62+1x^64+1x^66+1x^70

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.