The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+138x^13+84x^14+136x^15+15x^16+84x^17+28x^18+24x^19+2x^21

The gray image is a linear code over GF(2) with n=60, k=9 and d=26.
As d=26 is an upper bound for linear (60,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.11 in 0.016 seconds.