The generator matrix

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

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+30x^26+26x^28+2x^30+5x^32

The gray image is a linear code over GF(2) with n=54, k=6 and d=26.
As d=26 is an upper bound for linear (54,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.00282 seconds.