The generator matrix

 1  0  0  0  1  1  1  1  X  1  1  X  1  0  X  X  0  0  X  1  X  1  1  1  X  1  X  1  1  0  X  0  1  1  1  1  1  1  0  X  0  0  0  X  1  1  1  1  1  0  1
 0  1  0  0  0  1  X  0  0  1  1  1 X+1  1  1  1  X  1  0  0  1  X  1  1  X  1  1  X X+1  0  0  1  X  1  X  0 X+1  X  0  1  X  0  1  1  X X+1  1  1  1  X  0
 0  0  1  0  1  1  1  X  1  X  0  0  1  1 X+1  0  1  X  0  1 X+1 X+1 X+1  0  0  1  1  X  1  0  1  X  0  X  1  X  0 X+1  0  1  1  1 X+1  X  0  X  1  0  X  0  0
 0  0  0  1  1  0  0  1  1 X+1  X X+1  1 X+1  X  0  0  1  1 X+1 X+1  0  1  X  1  X  0 X+1  1  1  1  0 X+1 X+1 X+1  X  X  X  1  X X+1  X  0  X  0  X  1  X  0  X  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  X  0  X  0  X  X  X  0  0  X  0  X  X  X  0  X  X  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  X  0  X  X  X  X  0  0  X  0  X  0  0  X  X  X  X  0  0  0  0  0  0  X  X  X  X  0  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+53x^44+94x^45+63x^46+44x^47+94x^48+122x^49+89x^50+40x^51+53x^52+98x^53+47x^54+24x^55+27x^56+54x^57+31x^58+12x^59+26x^60+16x^61+22x^62+4x^63+2x^64+4x^66+4x^67

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 0.115 seconds.