The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X  X  2  0  0  X  1  1  1  1  1
 0  X  0  X  0  0  X X+2  0  2  X X+2  0  X  X  0  X X+2 X+2  X X+2  2 X+2
 0  0  X  X  0 X+2  X  0  0  X  X  2 X+2 X+2  X  X  0  0  2  X  2  X  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  0  2  0  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  2  0  2  2  2  2  2  0
 0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  2  2  0  0  2  2  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  2  2  0  2  0  0  2
 0  0  0  0  0  0  0  2  0  2  2  0  2  2  2  2  0  0  2  2  2  2  2
 0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  2  2  0  2  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+178x^16+296x^18+128x^19+951x^20+512x^21+1576x^22+768x^23+1773x^24+512x^25+888x^26+128x^27+374x^28+56x^30+47x^32+3x^36+1x^40

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 1.04 seconds.