The generator matrix

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

generates a code of length 8 over GR(16,4) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+72x^19+21x^20+96x^21+144x^23+213x^24+288x^25+168x^27+15x^28+6x^32

The gray image is a code over GF(4) with n=32, k=5 and d=19.
This code was found by Heurico 1.16 in -6.87e-008 seconds.