The generator matrix

 1  0  0  1
 0  1  0  1
 0  0  1 a^2+2a+1

generates a code of length 4 over GR(64,4) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+336x^14+42x^16+10752x^21+4704x^22+168x^24+154112x^28+75264x^29+16464x^30+301x^32

The gray image is a code over GF(8) with n=32, k=6 and d=14.
This code was found by Heurico 1.16 in 0.128 seconds.