The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+100x^26+404x^27+417x^28+312x^29+401x^30+232x^31+93x^32+56x^33+10x^34+20x^35+1x^36+1x^38

The gray image is a code over GF(2) with n=232, k=11 and d=104.
This code was found by Heurico 1.16 in 0.032 seconds.