The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+80x^25+648x^26+1232x^27+1340x^28+1712x^29+1404x^30+1032x^31+499x^32+144x^33+60x^34+24x^35+16x^36

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 0.25 seconds.