The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+156x^23+1009x^24+3330x^25+7269x^26+15968x^27+23377x^28+28436x^29+23939x^30+16100x^31+7298x^32+3042x^33+771x^34+282x^35+75x^36+8x^37+5x^38+4x^39+2x^43

The gray image is a code over GF(2) with n=232, k=17 and d=92.
This code was found by Heurico 1.16 in 50.2 seconds.