The generator matrix

 1  0  1  1 X^2+X  1  1  1  X  1  1 X^2+2 X^2+2  1  1  1
 0  1  1 X^2+X  1 X+3 X^2+3 X^2  1  X X^2+X+3  1  X X+1 X+3 X+3
 0  0  X  0  2 X^2 X^2+2  X  X X+2 X^2+X X^2+X+2 X^2+X X^2+X X+2 X^2
 0  0  0  2  2  0  2  2  2  0  2  0  2  0  2  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+140x^13+484x^14+770x^15+1347x^16+752x^17+456x^18+108x^19+12x^20+20x^21+4x^22+2x^23

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 0.032 seconds.