The generator matrix

 1  0  1  1  1  0  1  1  2  1  1  1 X+2  X  X X+2  2  1  2  1  1  1  1  1
 0  1  1  0 X+1  1  0 X+1  1  X X+3  3  1  1  1  1  X  0  X X+3  0 X+2 X+1  0
 0  0  X  0  X  0  X  0  X X+2  0  2  X X+2  0  2  X X+2  2  0  2  2  X  0
 0  0  0  X  X X+2  X  0  0  2 X+2  0 X+2  2  X  2  0 X+2 X+2 X+2 X+2  2  X  0
 0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  0  0  0  0
 0  0  0  0  0  2  0  0  2  2  2  0  0  0  2  2  0  2  0  0  2  0  2  0
 0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  0  0  2  2  2  2  2  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  2  2  0  2  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+57x^16+66x^17+217x^18+422x^19+651x^20+1306x^21+1818x^22+2262x^23+2668x^24+2350x^25+1881x^26+1346x^27+668x^28+366x^29+158x^30+66x^31+50x^32+8x^33+21x^34+1x^36+1x^42

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 2.73 seconds.