The generator matrix

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

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+72x^13+261x^14+368x^15+709x^16+308x^17+224x^18+72x^19+18x^20+12x^21+3x^22

The gray image is a code over GF(2) with n=128, k=11 and d=52.
This code was found by Heurico 1.16 in 0.016 seconds.