The generator matrix

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

generates a code of length 23 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+166x^16+482x^17+1482x^18+2648x^19+4868x^20+7562x^21+9650x^22+11264x^23+10213x^24+7894x^25+4880x^26+2408x^27+1291x^28+446x^29+210x^30+64x^31+4x^32+2x^34+1x^36

The gray image is a code over GF(2) with n=92, k=16 and d=32.
This code was found by Heurico 1.13 in 13.1 seconds.