The generator matrix

 1  0  0  1  1  1  X  1  0  1  1  2 X+2  1  1  X  0  1 X+2  1 X+2  1  1
 0  1  0  1  0 X+3  1 X+2  0 X+3  0  1  1  3  X  1  1  1  1  1  1  0  0
 0  0  1  1  1  0  1  X  1 X+2 X+1 X+1  0 X+3 X+1  1  2 X+2  1  2 X+3  0  0
 0  0  0  X  0 X+2  2  0 X+2 X+2  2 X+2  X  2  X X+2  0  0  0  2  2  0  0
 0  0  0  0  X  0  2 X+2 X+2 X+2  0  2 X+2  2  0  X  X  2 X+2  X X+2  0  0
 0  0  0  0  0  2  2  2  2  0  2  2  2  0  2  0  2  2  0  2  2  2  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+59x^16+154x^17+401x^18+722x^19+1216x^20+1820x^21+2439x^22+2716x^23+2405x^24+1986x^25+1231x^26+650x^27+340x^28+136x^29+89x^30+8x^31+10x^32+1x^40

The gray image is a code over GF(2) with n=92, k=14 and d=32.
This code was found by Heurico 1.16 in 2.6 seconds.