The generator matrix

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

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+62x^13+34x^14+82x^15+22x^16+34x^17+6x^18+14x^19+1x^24

The gray image is a linear code over GF(2) with n=60, k=8 and d=26.
As d=27 is an upper bound for linear (60,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.00402 seconds.