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.