The generator matrix

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

generates a code of length 24 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+148x^17+625x^18+1512x^19+2787x^20+4906x^21+7842x^22+9038x^23+11237x^24+9782x^25+7941x^26+4830x^27+2797x^28+1318x^29+485x^30+202x^31+74x^32+6x^33+2x^34+2x^35+1x^38

The gray image is a code over GF(2) with n=96, k=16 and d=34.
This code was found by Heurico 1.13 in 14.4 seconds.