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

generates a code of length 61 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+128x^54+122x^56+232x^58+20x^60+185x^62+72x^64+163x^66+12x^68+54x^70+21x^72+2x^74+1x^78+7x^80+3x^82+1x^88

The gray image is a linear code over GF(2) with n=122, k=10 and d=54.
This code was found by Heurico 1.16 in 10.5 seconds.