The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 2X  X  X  2 2X+2  1  0  1  1  2  X  1
 0  X  0  X  0 2X+2 3X+2 3X+2 2X+2  2  0  X 2X 3X X+2 2X+2 X+2  2 X+2 X+2  X  X  0  X 2X 2X  X  X 3X+2
 0  0  X  X  2  X 3X+2  0 2X+2 3X+2 2X X+2 X+2 X+2 2X+2 X+2 2X+2  X 2X+2 3X 3X+2  2 X+2 2X  X  X  0 3X X+2
 0  0  0 2X  0  0 2X 2X 2X 2X 2X  0 2X  0 2X 2X  0  0  0  0  0 2X  0  0 2X  0 2X 2X  0
 0  0  0  0 2X 2X 2X 2X  0 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X 2X  0 2X 2X 2X  0 2X  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+178x^25+270x^26+568x^27+691x^28+762x^29+756x^30+468x^31+130x^32+156x^33+62x^34+36x^35+9x^36+6x^37+1x^40+2x^41

The gray image is a code over GF(2) with n=232, k=12 and d=100.
This code was found by Heurico 1.16 in 41.4 seconds.