The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  X  X  X
 0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0
 0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0
 0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0

generates a code of length 15 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+14x^14+96x^15+15x^16+2x^22

The gray image is a linear code over GF(2) with n=120, k=7 and d=56.
This code was found by Heurico 1.16 in 3.62e-008 seconds.