The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+74x^9+798x^10+2790x^11+11477x^12+28940x^13+42772x^14+29172x^15+11498x^16+2666x^17+766x^18+102x^19+15x^20+1x^24

The gray image is a code over GF(2) with n=112, k=17 and d=36.
This code was found by Heurico 1.16 in 15.2 seconds.