The generator matrix

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

generates a code of length 16 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+304x^11+1767x^12+7502x^13+25370x^14+57286x^15+77342x^16+57836x^17+25356x^18+7356x^19+1689x^20+262x^21+58x^22+14x^23+1x^24

The gray image is a code over GF(2) with n=128, k=18 and d=44.
This code was found by Heurico 1.16 in 87.7 seconds.