The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+670x^12+1360x^14+1455x^16+560x^18+50x^20

The gray image is a linear code over GF(2) with n=60, k=12 and d=24.
As d=24 is an upper bound for linear (60,12,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 12.
This code was found by Heurico 1.16 in 21.7 seconds.