The generator matrix

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

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+161x^24+852x^25+1986x^26+4100x^27+5942x^28+6650x^29+6166x^30+4084x^31+1752x^32+768x^33+218x^34+52x^35+24x^36+2x^37+6x^38+4x^39

The gray image is a code over GF(2) with n=232, k=15 and d=96.
This code was found by Heurico 1.16 in 3.72 seconds.