The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+110x^25+682x^26+964x^27+1532x^28+1730x^29+1604x^30+788x^31+505x^32+170x^33+80x^34+10x^36+14x^37+2x^38

The gray image is a code over GF(2) with n=232, k=13 and d=100.
This code was found by Heurico 1.16 in 0.234 seconds.