The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+204x^20+216x^22+428x^24+336x^26+468x^28+216x^30+159x^32+16x^36+4x^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 29.4 seconds.