The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  0  2  1  2  0  0  1  2  0  2  0  0  2  2
 0  1  0  0  0  1  1  1  2  3  1  0  1  1  2  1  0  1  3  1  1  0  1  0  1  1
 0  0  1  0  1  1  0  1  0  1  0  3  1  2  0  2  1  3  3  1  2  0  0  1  1  1
 0  0  0  1  1  0  1  1  1  3  0  2  2  3  1  3  3  3  1  0  3  1  0  2  2  2
 0  0  0  0  2  0  0  0  0  2  2  2  0  0  0  2  0  2  0  2  2  2  2  0  0  0
 0  0  0  0  0  2  0  2  2  2  0  2  0  2  2  0  2  2  0  2  2  2  2  0  0  2
 0  0  0  0  0  0  2  2  2  0  2  2  0  2  0  2  0  2  0  0  0  2  2  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+177x^20+274x^22+395x^24+374x^26+392x^28+270x^30+115x^32+42x^34+7x^36+1x^40

The gray image is a code over GF(2) with n=52, k=11 and d=20.
This code was found by Heurico 1.16 in 0.197 seconds.