The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  2  1  1 X+2  X X+2  2  1  1  1  1  1  1  X  X  1  1  X
 0  1  1 X+2 X+1  1  3  2  1  2  1  1  X X+3  1  1  1  1  X X+3  2  3  X X+1  X  X X+1  1  2
 0  0  X  0  2  0  2  X  X X+2 X+2 X+2  X  X  0  X  X  2  2  0  0  2  X  X  X X+2  0  X  X
 0  0  0  2  2  2  0  2  2  0  2  0  0  2  0  0  2  2  0  0  2  2  2  0  2  2  2  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+102x^26+64x^27+110x^28+76x^30+64x^31+67x^32+14x^34+14x^36

The gray image is a code over GF(2) with n=116, k=9 and d=52.
This code was found by Heurico 1.16 in 0.0284 seconds.