The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+246x^26+331x^28+256x^30+93x^32+67x^34+23x^36+6x^38+1x^42

The gray image is a code over GF(2) with n=116, k=10 and d=52.
This code was found by Heurico 1.16 in 0.0566 seconds.