The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  1  1  1  1  1  X  1  X  1  1  X  1  X
 0  X  0 X+2  2 3X+2 2X+2  X  0 3X 2X+2 3X+2 X+2  X 2X 3X+2  2  X  0 X+2  2 X+2  X  X 3X 3X 3X 2X 3X+2
 0  0 2X+2  0  2  2 2X  2  0 2X  0 2X+2  0 2X  2  2  2 2X+2 2X  2 2X  0 2X+2  2  2  0 2X 2X+2  2
 0  0  0 2X  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X
 0  0  0  0 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X  0 2X  0  0  0  0 2X  0 2X 2X 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+72x^25+152x^26+174x^27+366x^28+542x^29+363x^30+170x^31+127x^32+56x^33+8x^34+6x^35+2x^36+2x^37+4x^38+2x^39+1x^46

The gray image is a code over GF(2) with n=232, k=11 and d=100.
This code was found by Heurico 1.16 in 0.265 seconds.