The generator matrix

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

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+174x^10+1564x^11+6699x^12+24512x^13+58004x^14+79980x^15+58438x^16+24480x^17+6558x^18+1524x^19+173x^20+32x^21+4x^23+1x^24

The gray image is a code over GF(2) with n=120, k=18 and d=40.
This code was found by Heurico 1.16 in 69.2 seconds.