The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1  X 3X  1  1  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  0  1 X+2 2X+2  0
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X  0 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+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 6.87e-008 seconds.