The generator matrix

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

generates a code of length 23 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+96x^12+274x^16+1128x^20+4096x^23+1880x^24+528x^28+149x^32+40x^36

The gray image is a code over GF(2) with n=92, k=13 and d=24.
This code was found by Heurico 1.16 in 0.551 seconds.