The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+98x^10+766x^11+3475x^12+12002x^13+28887x^14+40276x^15+29473x^16+11980x^17+3200x^18+750x^19+139x^20+18x^21+7x^22

The gray image is a code over GF(2) with n=120, k=17 and d=40.
This code was found by Heurico 1.16 in 18.4 seconds.