The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^13+229x^14+432x^15+635x^16+428x^17+215x^18+48x^19+4x^20+2x^21+3x^22+1x^26

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 0.015 seconds.