The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+32x^20+82x^21+85x^22+72x^23+106x^24+112x^25+86x^26+80x^27+86x^28+108x^29+72x^30+40x^31+29x^32+16x^33+10x^34+2x^36+2x^37+3x^38

The gray image is a code over GF(2) with n=52, k=10 and d=20.
This code was found by Heurico 1.10 in 0.016 seconds.