The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  1  X  0  1  1  X  1  0  X  1  X  1  1
 0  X  0 X+2  0 X+2  0 X+2  X  X  2 X+2 X+2  X  0 X+2 X+2  0  X X+2 X+2 X+2  0 X+2
 0  0  2  0  0  0  0  0  0  0  2  0  2  2  0  0  2  0  2  2  0  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  0  0  2  2  2  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  0  2  2  0  2  2  2  0
 0  0  0  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  0  0  2  2  0  2
 0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  0  2  2  2  0  2  2
 0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  0  0  0  2  2  2
 0  0  0  0  0  0  0  0  0  2  0  2  0  0  2  2  0  2  0  2  0  2  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+138x^16+96x^18+64x^19+568x^20+576x^21+672x^22+1408x^23+1132x^24+1408x^25+672x^26+576x^27+608x^28+64x^29+96x^30+101x^32+8x^36+4x^40

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 9.5 seconds.