The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+8x^29+5x^30+1x^32+1x^34

The gray image is a code over GF(2) with n=112, k=4 and d=58.
This code was found by Heurico 1.16 in 0.00475 seconds.