The generator matrix

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

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+162x^11+1055x^12+2782x^13+7268x^14+10132x^15+7485x^16+2748x^17+916x^18+170x^19+43x^20+6x^21

The gray image is a code over GF(2) with n=120, k=15 and d=44.
This code was found by Heurico 1.16 in 1.44 seconds.