The generator matrix

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

generates a code of length 10 over GR(16,4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+480x^22+318x^24+1440x^26+1488x^28+7968x^30+2223x^32+2400x^34+48x^36+18x^40

The gray image is a code over GF(4) with n=40, k=7 and d=22.
This code was found by Heurico 1.16 in 135 seconds.