The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+180x^18+308x^19+931x^20+1004x^21+2056x^22+2256x^23+2865x^24+2296x^25+2104x^26+1012x^27+893x^28+284x^29+171x^30+8x^31+14x^32+1x^46

The gray image is a code over GF(2) with n=96, k=14 and d=36.
This code was found by Heurico 1.16 in 3.17 seconds.