The generator matrix

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

generates a code of length 15 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+86x^11+482x^12+1444x^13+3614x^14+5052x^15+3816x^16+1352x^17+392x^18+126x^19+12x^20+4x^21+2x^22+1x^24

The gray image is a code over GF(2) with n=120, k=14 and d=44.
This code was found by Heurico 1.16 in 0.39 seconds.