The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2X+2) 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 0.015 seconds.