The generator matrix

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

generates a code of length 26 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+69x^16+128x^17+222x^18+246x^19+455x^20+760x^21+981x^22+1314x^23+1496x^24+1640x^25+1689x^26+1716x^27+1558x^28+1240x^29+1002x^30+732x^31+464x^32+312x^33+184x^34+86x^35+51x^36+16x^37+17x^38+2x^39+2x^40+1x^42

The gray image is a code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.16 in 12.2 seconds.