The generator matrix

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

generates a code of length 44 over Z2[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+51x^32+86x^33+169x^34+266x^35+430x^36+486x^37+600x^38+812x^39+890x^40+1074x^41+1229x^42+1272x^43+1360x^44+1398x^45+1317x^46+1218x^47+1004x^48+842x^49+584x^50+442x^51+302x^52+194x^53+162x^54+80x^55+54x^56+14x^57+33x^58+4x^59+4x^60+2x^61+1x^62+2x^63+1x^66

The gray image is a linear code over GF(2) with n=88, k=14 and d=32.
This code was found by Heurico 1.16 in 37.8 seconds.