The generator matrix

 1  0  0  0  1  1  1 2X  1  1  X  X  1 3X  1 3X  1 2X+2  1  1 2X X+2 3X  1 3X  1 X+2 2X+2  1
 0  1  0  0 2X  X 3X+2 3X 2X+3 X+1  1  1 3X+3  1  3 3X 2X+1  1  1  2 2X  1 2X+2 2X  1 3X+2 2X  1  X
 0  0  1  0 2X+1 2X  1  1  3  3 2X+2  3 3X X+3 2X  1 X+2  X 3X+3 X+3  1 X+2  1 3X+2 3X+1 3X+1  0  3  2
 0  0  0  1  1 2X+1 2X  1  X X+1  3 X+3 2X+2 X+2 3X+3 X+3 3X+1 3X+2 2X+2 X+3 X+2  X  3 2X+2 3X+1 3X  1 2X+3 2X+3

generates a code of length 29 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+317x^24+1908x^25+4012x^26+8124x^27+10777x^28+14720x^29+11694x^30+8272x^31+3502x^32+1708x^33+354x^34+84x^35+59x^36+2x^38+2x^42

The gray image is a code over GF(2) with n=232, k=16 and d=96.
This code was found by Heurico 1.16 in 14.3 seconds.