The generator matrix

 1  0  1  1  1 2X 3X+2  1  1  1  1  X  1 2X+2 2X+2
 0  1 X+1 X+2 2X+3  1  1 2X 3X+2 X+1  3 3X  1  X  1
 0  0 2X+2  2 2X 2X+2  0 2X+2  0 2X 2X+2  2  2 2X+2  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+150x^13+212x^14+356x^15+143x^16+120x^17+28x^18+12x^19+2x^21

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 0.032 seconds.