The generator matrix

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

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+128x^13+532x^14+658x^15+1507x^16+632x^17+504x^18+92x^19+12x^20+24x^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 0.047 seconds.