The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  0  1  1  0  2  1  1  1  1  2  1  1  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0  3  1  3  0  1  2  3  3  3  1  0  0  0  0  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  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  0  0  2  2  2  2  0  0  0  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  0  2  0  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  2  0  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  0  0  2  2  0  0  2  2  2  0  0  2  0  2  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  0  2  2  0  2  0  2  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  2  0  2  2  0  2  0  0  0  2  2  2  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  0  2  0  2  2  0  0  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+330x^16+192x^18+22x^21+640x^22+616x^24+554x^25+368x^26+32x^28+2044x^29+557x^32+1332x^33+672x^34+480x^36+142x^37+32x^40+2x^41+176x^42

The gray image is a code over GF(2) with n=58, k=13 and d=16.
This code was found by Heurico 1.16 in 1.85 seconds.