The generator matrix

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

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+14x^14+32x^15+15x^16+2x^22

The gray image is a linear code over GF(2) with n=60, k=6 and d=28.
This code was found by Heurico 1.16 in 0.000773 seconds.