The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+53x^16+108x^17+209x^18+332x^19+534x^20+746x^21+965x^22+1150x^23+1418x^24+1700x^25+1738x^26+1788x^27+1553x^28+1248x^29+1002x^30+736x^31+476x^32+272x^33+165x^34+88x^35+56x^36+22x^37+17x^38+2x^39+4x^40+1x^44

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 13 seconds.