The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  1  1  1  1  0  0  1  1  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0  3  1  0  3  1  0  3  1  0  1  1  3  3  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  0  0  2  0  2  2  2  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  0  2  2  2  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  0  2  0  2  0  2  2  2  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  2  0  0  2  2  0  2  2  0  2  2  0  2  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  0  2  0  2  0  0  2  2  2  0  2  2  2  0  0  0
 0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  0  0  2  0  2  2  0  2  2  2  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+118x^16+69x^18+324x^20+144x^21+320x^22+128x^23+844x^24+1472x^25+1000x^26+896x^27+1404x^28+2912x^29+1416x^30+896x^31+1025x^32+1472x^33+866x^34+128x^35+316x^36+144x^37+304x^38+60x^40+112x^42+4x^44+8x^46+1x^50

The gray image is a code over GF(2) with n=58, k=14 and d=16.
This code was found by Heurico 1.16 in 7.08 seconds.