The generator matrix

 1  0  1  1  1  0  1  1  X  1 X+2  1  1  X  0  1  2  X  1  1  1  X  1  X
 0  1  1  0 X+1  1  X X+3  1 X+2  1  3  2  2  1 X+1  1  1 X+2  3  1  2  0  0
 0  0  X X+2  0 X+2  X X+2  X  0  2  0  X  X  0  0  X  X  2  0  X  X  2  0
 0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  2  2  0  2  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  2
 0  0  0  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  0  0  2  2
 0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  0  2  2  2  0  0  2
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  0  0  0  0  2  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+116x^16+236x^18+160x^19+1001x^20+928x^21+2204x^22+1984x^23+3112x^24+1984x^25+2180x^26+928x^27+1059x^28+160x^29+244x^30+83x^32+3x^36+1x^44

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 2.8 seconds.