The generator matrix

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

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+400x^11+1762x^12+5998x^13+14946x^14+19242x^15+15135x^16+5932x^17+1676x^18+420x^19+14x^20+6x^21+2x^22+2x^23

The gray image is a code over GF(2) with n=120, k=16 and d=44.
This code was found by Heurico 1.16 in 5.53 seconds.