The generator matrix

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

generates a code of length 16 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+92x^13+473x^14+842x^15+1451x^16+638x^17+406x^18+150x^19+36x^20+6x^21+1x^22

The gray image is a code over GF(2) with n=128, k=12 and d=52.
This code was found by Heurico 1.16 in 0.031 seconds.