The generator matrix

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

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+122x^44+84x^46+187x^48+124x^50+181x^52+108x^54+108x^56+68x^58+24x^60+6x^64+9x^68+2x^72

The gray image is a linear code over GF(2) with n=102, k=10 and d=44.
This code was found by Heurico 1.16 in 0.174 seconds.