The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  0  X  1  1  0  1  X  1
 0  X  0  0  0  0  0  0  2  2  X X+2  X  X  0  X X+2 X+2  2  0 X+2 X+2 X+2
 0  0  X  0  0  0  0  0  0  0  0  0  X  2 X+2 X+2  2  X  X  2 X+2  2  X
 0  0  0  X  0  0  2 X+2  X  X  X  X  X  X X+2  X  0  X X+2  0  X X+2  2
 0  0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  X  0  0  2  0  2  0  X  X  X  X
 0  0  0  0  0  X  X  2 X+2  X X+2  2  0 X+2 X+2  2  X  0  0  2  0  2 X+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+82x^16+146x^17+209x^18+358x^19+469x^20+882x^21+1252x^22+1338x^23+1281x^24+890x^25+584x^26+330x^27+161x^28+126x^29+32x^30+22x^31+20x^32+4x^33+3x^34+2x^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 1.18 seconds.