The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1  X X+2  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  0  1 X^2+X X^2+2  0
 0  0  2  0  2  0  2  0  2  2  0  2  2  2  2  0
 0  0  0  2  2  2  2  0  0  0  2  0  2  2  0  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+24x^13+66x^14+368x^15+123x^16+352x^17+60x^18+16x^19+4x^20+8x^21+2x^22

The gray image is a code over GF(2) with n=128, k=10 and d=52.
This code was found by Heurico 1.16 in 0.016 seconds.