The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  X  1  1  1 X+2 X+2 X+2  1  1  1  1  1  1  2  2 X+2  1  1
 0  1  0  2  3  1  1  0  3  1 X+2  1 X+1  X  2  1 X+2  0 X+3  X  1 X+3 X+1 X+3  X  1  1 X+3  0
 0  0  1 X+3 X+1  2 X+1 X+2  3  3  1  0  2  X  1 X+3  1  1 X+1  0  X  X  X  3  1 X+2 X+2 X+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+46x^26+136x^27+79x^28+46x^29+51x^30+88x^31+26x^32+6x^33+15x^34+12x^35+6x^36

The gray image is a code over GF(2) with n=116, k=9 and d=52.
This code was found by Heurico 1.13 in 0.015 seconds.