The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+88x^11+861x^12+4134x^13+12068x^14+29744x^15+36698x^16+30806x^17+11904x^18+3704x^19+903x^20+130x^21+28x^22+1x^24+2x^25

The gray image is a code over GF(2) with n=128, k=17 and d=44.
This code was found by Heurico 1.16 in 19.9 seconds.