The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1 X^2+2 X+2  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X+2 X^2+X+3  3  1  1  0 X^2+X  2
 0  0  2  2  0  2  2  0  0  2  2  0  2  0  0

generates a code of length 15 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+32x^13+190x^14+64x^15+191x^16+32x^17+2x^22

The gray image is a code over GF(2) with n=120, k=9 and d=52.
This code was found by Heurico 1.16 in 0 seconds.