The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  X  1  0  X  1  1  1  1  0  0  X  1  X  1  1  0  X  1  0  1  0  X  1  X  1  1  X  1  X  0  X  1
 0  1  0  0  0  0  0  0  0  1  1  1  0  X  1  X  0 X+1  1  1  1  X  1  1  1 X+1  0  1  1  1  1  0  X  1  X  X  X  X  0 X+1  1  1  1  1
 0  0  1  0  0  0  1  1  1  1  X  1  1  0  X  1  0  0 X+1  0 X+1  X X+1 X+1  0 X+1  1  X  1  0  1  1  1  1  0  0 X+1 X+1  0  1 X+1 X+1  X  X
 0  0  0  1  0  1  1  0  1  0 X+1 X+1  X  0 X+1  1  1  1  1 X+1  0  1  0 X+1  X  X  0  1  1 X+1  X X+1  0 X+1 X+1  X  0  X  1  0  1 X+1  X  1
 0  0  0  0  1  1  0  1  1  X  0  X X+1  1 X+1  0  0  1 X+1  0  1 X+1  0  X  1  1  X  0 X+1  1  X X+1  0  0  X  1  X  1  0  0 X+1  0  X  0
 0  0  0  0  0  X  0  0  0  X  0  X  X  X  X  X  X  0  X  X  0  X  0  0  0  X  0  0  0  X  0  X  X  X  0  X  X  0  X  X  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  X  0  X  X  0  0  X  X  X  X  0  X  0  X  X
 0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  X  X  0  0  0  0  X  X  X  X  X  X  X  0  X  X  0  X  X  0  0  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  0  0  X  X  X  0  0  X  0  0  0  0  X  0  X  0  X  0  0  X  0  X  X  X  X  0  X  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+82x^33+179x^34+280x^35+439x^36+550x^37+615x^38+794x^39+937x^40+1056x^41+1268x^42+1266x^43+1283x^44+1376x^45+1259x^46+1154x^47+1044x^48+774x^49+643x^50+528x^51+341x^52+234x^53+117x^54+66x^55+41x^56+24x^57+14x^58+6x^59+9x^60+1x^62+2x^63+1x^64

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 99.1 seconds.