The generator matrix
1 0 1 1 1 X 1 1 0 1 1 X 1 1 1 1 0 X 1 1 1 1 0 X 1 1 1 1 0 X X X 0 1 1 1 1 0 X X X 0 1 1 1 1 X X 0 0 X 1
0 1 X+1 X 1 1 0 X+1 1 X 1 1 0 X X+1 1 1 1 0 X X+1 1 1 1 0 X X+1 1 1 1 0 X X 0 X X+1 1 1 1 0 X X 0 X X+1 1 0 X X 1 1 0
generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+2x^54+8x^55+3x^56+2x^58
The gray image is a linear code over GF(2) with n=104, k=4 and d=54.
This code was found by Heurico 1.16 in 0.0163 seconds.