The generator matrix

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

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+148x^16+430x^18+64x^19+839x^20+512x^21+1616x^22+896x^23+1711x^24+512x^25+856x^26+64x^27+408x^28+104x^30+27x^32+2x^34+1x^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 1.1 seconds.