The generator matrix

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

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+71x^14+45x^16+8x^18+2x^20+1x^22

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 0.00493 seconds.