The generator matrix

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

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+68x^16+58x^17+137x^18+180x^19+302x^20+596x^21+849x^22+1204x^23+1344x^24+1208x^25+918x^26+636x^27+288x^28+172x^29+126x^30+28x^31+43x^32+14x^33+17x^34+2x^36+1x^38

The gray image is a code over GF(2) with n=96, k=13 and d=32.
This code was found by Heurico 1.16 in 1 seconds.