The generator matrix

 1  1  1  1  1  1  1  1  X  1  2  1  X  X  1
 0  X  0 X^2+X+2  0 X^2+X  0  X X^2+X  2  X X^2+X+2 X^2+X X^2+2  0
 0  0 X^2+2  0  0 X^2 X^2+2 X^2 X^2  2  0 X^2+2 X^2+2 X^2  0
 0  0  0 X^2+2 X^2+2 X^2 X^2  0 X^2  2 X^2+2  2 X^2 X^2  0
 0  0  0  0  2  0  0  2  2  2  0  0  2  0  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+36x^10+72x^11+129x^12+342x^13+603x^14+1720x^15+605x^16+372x^17+122x^18+48x^19+33x^20+6x^21+7x^22

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 0.047 seconds.