The generator matrix

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

generates a code of length 15 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+206x^10+1130x^11+4347x^12+12274x^13+27912x^14+38852x^15+28806x^16+12068x^17+4070x^18+1170x^19+189x^20+42x^21+4x^22+1x^24

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 17.6 seconds.