The generator matrix

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

generates a code of length 61 over Z2[X]/(X^2) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+116x^49+200x^50+306x^51+425x^52+532x^53+628x^54+702x^55+823x^56+890x^57+990x^58+970x^59+1006x^60+1058x^61+1116x^62+1086x^63+956x^64+922x^65+862x^66+772x^67+578x^68+458x^69+358x^70+216x^71+155x^72+112x^73+68x^74+40x^75+22x^76+8x^77+2x^78+4x^79+1x^80+1x^100

The gray image is a linear code over GF(2) with n=122, k=14 and d=49.
This code was found by Heurico 1.10 in 21.1 seconds.