The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+40x^20+62x^21+90x^22+98x^23+85x^24+98x^25+92x^26+110x^27+88x^28+82x^29+60x^30+46x^31+41x^32+14x^33+12x^34+2x^35+2x^38+1x^40

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 0.0413 seconds.