The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+109x^10+860x^11+3581x^12+11320x^13+28832x^14+41408x^15+29245x^16+11384x^17+3341x^18+804x^19+165x^20+16x^21+6x^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 18.5 seconds.