The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+100x^13+473x^14+818x^15+1451x^16+662x^17+406x^18+142x^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.