The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+100x^20+76x^22+274x^24+172x^26+188x^28+132x^30+59x^32+4x^34+16x^36+2x^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 0.0739 seconds.