The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+20x^29+2x^30+4x^31+3x^32+2x^34

The gray image is a code over GF(2) with n=116, k=5 and d=58.
This code was found by Heurico 1.16 in 0.00547 seconds.