The generator matrix
1 0 0 1 1
0 1 0 1 a
0 0 1 a^2+2a+1 a
generates a code of length 5 over GR(64,4) who´s minimum homogenous weight is 21.
Homogenous weight enumerator: w(x)=1x^0+560x^21+70x^24+11200x^28+7840x^29+175x^32+136192x^35+78400x^36+27440x^37+266x^40
The gray image is a code over GF(8) with n=40, k=6 and d=21.
This code was found by Heurico 1.16 in 0.201 seconds.