The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  0  2  2  2  2  0  0  0  0  0  0
 0  2  0  0  0  2  2  2  0  0  0  2  0  2  2  0  0  2  2  0  2  2  2  2  2  2  0  0  0
 0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  2  2  2  2  0
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  2  2  0  0  0  2  0  2  2  2  0  0  2  2

generates a code of length 29 over Z4 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+16x^29+8x^30+7x^32

The gray image is a code over GF(2) with n=58, k=5 and d=29.
This code was found by Heurico 1.16 in 0.0231 seconds.