The generator matrix

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

generates a code of length 26 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+41x^20+72x^21+75x^22+88x^23+103x^24+98x^25+92x^26+106x^27+83x^28+76x^29+72x^30+60x^31+24x^32+10x^33+16x^34+2x^35+4x^36+1x^38

The gray image is a code over GF(2) with n=52, k=10 and d=20.
This code was found by Heurico 1.16 in 0.0394 seconds.