The generator matrix

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

generates a code of length 26 over Z4 who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+88x^17+208x^18+346x^19+498x^20+700x^21+960x^22+1150x^23+1493x^24+1750x^25+1848x^26+1838x^27+1504x^28+1262x^29+1048x^30+678x^31+433x^32+282x^33+152x^34+80x^35+38x^36+14x^37+8x^38+4x^39+1x^40

The gray image is a code over GF(2) with n=52, k=14 and d=17.
This code was found by Heurico 1.16 in 15.9 seconds.