The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X
 0  X  0  0  0  0  0  X  0  0  X  X  0  0  X  X  0  X  0  X  0  X  0  X  X  0  X
 0  0  X  0  0  0  0  X  0  X  X  0  0  X  X  0  X  X  X  X  X  X  0  0  X  X  0
 0  0  0  X  0  0  0  X  X  0  X  0  X  X  0  X  X  0  X  0  X  0  X  X  X  0  X
 0  0  0  0  X  0  X  0  X  X  0  X  X  0  0  0  0  X  X  0  X  X  0  0  X  X  0
 0  0  0  0  0  X  X  0  0  X  X  0  X  0  X  0  X  0  X  0  0  X  X  X  0  0  X

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+21x^24+32x^26+67x^28+6x^32+1x^52

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 0.00502 seconds.