The generator matrix

 1  1  1  1  1  1  X  X  X  1  1  X  1  1  1
 0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2
 0  0 X^2 X^2  0 X^2 X^2  0 X^2 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+3x^14+22x^15+3x^16+2x^19+1x^22

The gray image is a linear code over GF(2) with n=60, k=5 and d=28.
This code was found by Heurico 1.16 in 0.000626 seconds.