The generator matrix

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

generates a code of length 19 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+282x^13+1138x^14+2244x^15+4436x^16+7564x^17+10807x^18+12560x^19+10692x^20+7628x^21+4765x^22+2212x^23+838x^24+268x^25+89x^26+8x^27+2x^29+1x^30+1x^32

The gray image is a code over GF(2) with n=76, k=16 and d=26.
This code was found by Heurico 1.13 in 16.9 seconds.