The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+22x^28+8x^29+22x^30+8x^31+1x^32+2x^34

The gray image is a code over GF(2) with n=116, k=6 and d=56.
This code was found by Heurico 1.16 in 0.00372 seconds.