The generator matrix

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

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+78x^24+496x^25+968x^26+2304x^27+2517x^28+3690x^29+2638x^30+2202x^31+844x^32+484x^33+102x^34+36x^35+15x^36+2x^37+2x^38+2x^39+1x^40+2x^42

The gray image is a code over GF(2) with n=232, k=14 and d=96.
This code was found by Heurico 1.16 in 1.01 seconds.