The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+304x^24+1966x^25+3937x^26+8004x^27+11286x^28+14116x^29+11886x^30+8396x^31+3515x^32+1556x^33+405x^34+128x^35+22x^36+8x^37+4x^38+2x^41

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 13.5 seconds.