The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  0  1  1  1  1  0
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  1  0 X+1 X+1  0  1
 0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  0  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  2  0  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  0  0  0  2  0  2  0  2  2
 0  0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  2  0  0  2  2  2  0  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  0  2  0  2  0  0  2  2  2
 0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  0  2  2  2  2
 0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+184x^16+144x^18+256x^19+448x^20+1792x^21+624x^22+4096x^23+1246x^24+4096x^25+624x^26+1792x^27+560x^28+256x^29+144x^30+103x^32+16x^36+2x^40

The gray image is a code over GF(2) with n=96, k=14 and d=32.
This code was found by Heurico 1.16 in 94.9 seconds.