The generator matrix

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

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+60x^41+154x^42+210x^43+398x^44+482x^45+590x^46+732x^47+784x^48+860x^49+962x^50+1122x^51+1137x^52+1234x^53+1171x^54+1176x^55+1123x^56+940x^57+859x^58+664x^59+527x^60+370x^61+313x^62+234x^63+118x^64+84x^65+45x^66+20x^67+6x^68+2x^69+2x^70+2x^71+2x^80

The gray image is a linear code over GF(2) with n=106, k=14 and d=41.
This code was found by an older version of Heurico in 0 seconds.