The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+15x^14+96x^15+15x^16+1x^30

The gray image is a linear code over GF(2) with n=60, k=7 and d=28.
As d=28 is an upper bound for linear (60,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.00119 seconds.