The generator matrix

 1  0  0  1  1  1  X  1  1  2  1 X+2  1  2  1  1  2 X+2  1  1  1  1  1  1
 0  1  0  1 X+2 X+3  1  0  3  1  X  1  1  X X+3 X+1  1  1  0  1  2  3  1  0
 0  0  1  1 X+3 X+2  1 X+2 X+1  X  1 X+1  X  1  1  0  1  0 X+1  1  X  0  1  0
 0  0  0  2  0  0  0  0  0  0  2  2  2  0  2  0  2  2  2  2  0  2  0  0
 0  0  0  0  2  0  0  0  0  2  2  2  0  0  0  2  0  2  0  2  0  2  0  0
 0  0  0  0  0  2  0  0  2  2  0  2  0  2  2  0  2  0  2  0  0  0  0  0
 0  0  0  0  0  0  2  0  2  0  0  2  2  0  0  2  2  2  2  0  2  2  0  0
 0  0  0  0  0  0  0  2  2  2  0  0  2  2  0  2  2  0  2  2  0  2  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+20x^16+56x^17+170x^18+384x^19+735x^20+1168x^21+2144x^22+1968x^23+3076x^24+1984x^25+2156x^26+1184x^27+742x^28+368x^29+128x^30+48x^31+31x^32+8x^33+10x^34+3x^36

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 2.18 seconds.