The generator matrix

 1  0  0  0  0  0  0  1  1  1  X  1  X  1  1  X  1  1  0  1  1  X  1  X  1  1  0  X  1  X  1  X  1  1  0  1  1  0  1  0  1  X  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  1  1  1  1 X+1  1 X+1  1  1  1 X+1  X X+1  1  1  X  1  0
 0  0  1  0  0  0  0  0  0  0  0  0  X  X  1  1 X+1  1  1 X+1 X+1  0  X  1  1 X+1  X X+1  X  1  X  0  1 X+1  X  0  X  1  0  1 X+1  0  X  1
 0  0  0  1  0  0  0  0 X+1  X  1  1  X  1  1 X+1 X+1  X  1  X X+1  0  1 X+1 X+1  0  1  1  X  0 X+1  1  0  0  1  X  0  1  1  1  X  X  1  1
 0  0  0  0  1  0  0  0  1 X+1  1  0  1 X+1  X  X  1  1  1  0  X  0  1  0 X+1  1  0  1 X+1  0  X  X  1 X+1 X+1  X X+1  0  1  1  0  0  X  X
 0  0  0  0  0  1  0  1  0  1  1  1  X X+1  X  X  0 X+1  1  X X+1  1  X  X  0  1  0 X+1  0 X+1 X+1  1 X+1  1  X  1  0 X+1  1  X  1  X X+1  X
 0  0  0  0  0  0  1  1 X+1  0 X+1  X X+1 X+1  X  1  X  1  1  1  1 X+1  0  X  1  X  X X+1  1  0 X+1  1  X  1  0  X  0  1  0  X  1  1  1  0
 0  0  0  0  0  0  0  X  X  X  X  0  X  0  X  0  0  X  0  X  0  0  X  0  0  0  X  X  X  X  0  0  X  0  0  0  0  X  0  X  0  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+103x^32+182x^33+407x^34+542x^35+722x^36+956x^37+1266x^38+1506x^39+1857x^40+2234x^41+2367x^42+2720x^43+2829x^44+2672x^45+2480x^46+2372x^47+1967x^48+1706x^49+1225x^50+894x^51+700x^52+396x^53+286x^54+154x^55+123x^56+38x^57+33x^58+4x^59+13x^60+8x^61+5x^64

The gray image is a linear code over GF(2) with n=88, k=15 and d=32.
This code was found by Heurico 1.16 in 98.5 seconds.