The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X 0 0 0
0 X 0 0 0 X X X 0 0 0 X 0 X X X 0 0 0 X X X X 0 X X X
0 0 X 0 X X X 0 0 0 X X X X 0 0 0 X X X X 0 0 0 0 0 X
0 0 0 X X 0 X X 0 X X 0 0 X X 0 X X 0 0 X X 0 0 0 X X
generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.
Homogenous weight enumerator: w(x)=1x^0+12x^26+12x^28+4x^30+3x^32
The gray image is a linear code over GF(2) with n=54, k=5 and d=26.
This code was found by Heurico 1.16 in 0.00184 seconds.