The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  2  0  2  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  0  0  0  2  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  2  0  0  0  0  0  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  0  0  0  2  0  2  2  2  2  2
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  0  0  2  0  2  2  2  0  2  2  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  0  0  0  2  2  2  0  0  2  2  2
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  0  0  2  2  0  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  0  0  2  0

generates a code of length 28 over Z4 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+148x^20+255x^24+1240x^28+255x^32+148x^36+1x^56

The gray image is a code over GF(2) with n=56, k=11 and d=20.
This code was found by Heurico 1.16 in 1.92 seconds.