The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+57x^24+126x^25+237x^26+520x^27+742x^28+802x^29+741x^30+480x^31+193x^32+82x^33+55x^34+24x^35+14x^36+14x^37+7x^38+1x^40

The gray image is a code over GF(2) with n=232, k=12 and d=96.
This code was found by Heurico 1.16 in 0.14 seconds.