The generator matrix

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

generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+219x^44+282x^46+334x^48+266x^50+252x^52+244x^54+162x^56+132x^58+105x^60+34x^62+15x^64+2x^66

The gray image is a linear code over GF(2) with n=102, k=11 and d=44.
This code was found by Heurico 1.16 in 11.4 seconds.