The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X^2+X  X  X  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1  3 X+2  1  0  0  0
 0  0  2  0  0  0  2  2  0  0  2  0  0  2  0
 0  0  0  2  0  0  2  0  0  2  2  2  0  2  0
 0  0  0  0  2  0  2  2  2  2  0  0  2  0  0
 0  0  0  0  0  2  2  0  2  0  2  0  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+19x^10+54x^11+83x^12+322x^13+1185x^14+788x^15+1174x^16+316x^17+69x^18+54x^19+21x^20+2x^21+7x^22+1x^24

The gray image is a code over GF(2) with n=120, k=12 and d=40.
This code was found by Heurico 1.16 in 0.032 seconds.