The generator matrix

 1  0  1  1  1  0  1  1  2  1 X+2  1  0  1  1  1  X  X  0  X  1  1  1
 0  1  1  0 X+1  1 X+1  0  1  X  1 X+3  1  3  2  1 X+2  1  0  1  1  3  0
 0  0  X  0  0  0  X  X  X X+2 X+2  0  X  X  2 X+2  X X+2  X  X X+2  X  0
 0  0  0  X  0 X+2  X  X  2  2  X  X X+2  X X+2  0  X  0  0  2  2 X+2  0
 0  0  0  0  2  0  0  2  2  2  2  0  2  0  0  0  0  0  2  2  0  2  2
 0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  2  2
 0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  0  0  2  2  2  0  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+31x^16+78x^17+185x^18+414x^19+427x^20+1158x^21+894x^22+1806x^23+900x^24+1194x^25+428x^26+394x^27+164x^28+66x^29+26x^30+10x^31+12x^32+3x^34+1x^36

The gray image is a code over GF(2) with n=92, k=13 and d=32.
This code was found by Heurico 1.16 in 0.825 seconds.