The generator matrix

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

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+148x^13+185x^14+392x^15+151x^16+116x^17+14x^18+16x^19+1x^22

The gray image is a code over GF(2) with n=120, k=10 and d=52.
This code was found by Heurico 1.16 in 0.016 seconds.