The generator matrix

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

generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+18x^24+40x^25+16x^26+12x^28+16x^29+10x^30+1x^32+8x^33+4x^34+2x^38

The gray image is a linear code over GF(2) with n=54, k=7 and d=24.
As d=24 is an upper bound for linear (54,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.00274 seconds.