The generator matrix

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

generates a code of length 26 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+11x^24+8x^25+15x^26+22x^27+4x^28+1x^34+2x^35

The gray image is a linear code over GF(2) with n=52, k=6 and d=24.
This code was found by Heurico 1.16 in 0.00163 seconds.