The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+83x^26+88x^27+209x^28+336x^29+126x^30+88x^31+60x^32+31x^34+1x^36+1x^48

The gray image is a code over GF(2) with n=232, k=10 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.