The generator matrix

 1  0  1  1  1  0  1  1 X+2  1  1  X  1  0  1  X  1  X  1  2  1  1  X
 0  1  1  0 X+1  1  X X+3  1 X+2  3  1  0  1 X+3  2 X+1  1 X+2  X X+1 X+3  2
 0  0  X X+2  0 X+2  X X+2  0  0  0  X  2  2  X  X  0 X+2  0  X  0  X  X
 0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  0  0  2  0
 0  0  0  0  2  0  0  0  0  0  2  2  0  2  2  2  2  0  0  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  0  2  2  2  0
 0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  2  0  2  0  2  0  0  0  2  2  2  2  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  0  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+198x^16+32x^17+480x^18+512x^19+1220x^20+2016x^21+2336x^22+3072x^23+1872x^24+2016x^25+1440x^26+512x^27+504x^28+32x^29+96x^30+41x^32+4x^36

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 7.29 seconds.