The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  0  1  2  1  1  1  0  2  1  1  1  1  1  1  1  1
 0  1  0  1  0  1  1  0  0  1  1  1  1  0  2  1  1  2  3  0  1  3  1  3  0  2  3  0  0
 0  0  1  1  1  0  1  0  1  1  0  0  1  1  2  1  3  1  0  1  1  0  1  1  2  1  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  0  2  2  0  2  0  2  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  0  2  2  2  0  0  2  0  0  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  2  0  2  0  0  0  2  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  0  2  0  2  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  0  0  0  2  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  2  0  2  0  0  0  0  2  2  2  0  0  0  2  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  0  2  2  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  2  2  2  2  0  0  0  0

generates a code of length 29 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+135x^16+114x^18+779x^20+1148x^22+3403x^24+4414x^26+6587x^28+5608x^30+5458x^32+2638x^34+1737x^36+412x^38+281x^40+2x^42+49x^44+2x^48

The gray image is a code over GF(2) with n=58, k=15 and d=16.
This code was found by Heurico 1.16 in 20.8 seconds.