The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+X  1  1  0  1  1  1  1  1  1  1  1 X^2  X X^2  X  1  1  X
 0  1 X+1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1 X^2  X X^2+X+1  1 X^2  X X^2+X+1  1  1  1  1  1  0 X^2+X X^2+X
 0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+46x^26+32x^27+44x^28+2x^30+1x^32+2x^36

The gray image is a linear code over GF(2) with n=108, k=7 and d=52.
As d=53 is an upper bound for linear (108,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.00476 seconds.