The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+124x^11+1006x^12+3766x^13+12376x^14+28466x^15+39235x^16+29036x^17+12480x^18+3408x^19+938x^20+222x^21+8x^22+2x^23+4x^24

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 21 seconds.