The generator matrix

 1  0  0  1  1  1 2a+2  1  1  2
 0  1  0  1 2a+2 2a+3  1  a 3a+2  2
 0  0  1 3a+3  1  a  1  0  1 2a+2
 0  0  0  2 2a+2 2a 2a+2 2a  2 2a

generates a code of length 10 over GR(16,4) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+72x^21+480x^22+222x^24+648x^25+1440x^26+384x^27+912x^28+1944x^29+3360x^30+1152x^31+1359x^32+1944x^33+2400x^34+48x^36+18x^40

The gray image is a code over GF(4) with n=40, k=7 and d=21.
This code was found by Heurico 1.16 in 0.0811 seconds.