The generator matrix
1 0 0 1 1 1 1 1 1 1
0 1 0 1 a 2a+2 2a+3 2a+2 2 a+1
0 0 1 3a+3 a 1 a 3a+3 3a+2 a
0 0 0 2 0 2 2 2a 2a 2a
0 0 0 0 2 2a 2a+2 2a 0 2
generates a code of length 10 over GR(16,4) who´s minimum homogenous weight is 19.
Homogenous weight enumerator: w(x)=1x^0+120x^19+90x^20+192x^21+480x^23+2676x^24+1728x^25+3216x^27+15156x^28+5184x^29+7008x^31+22779x^32+5184x^33+1464x^35+210x^36+48x^40
The gray image is a code over GF(4) with n=40, k=8 and d=19.
This code was found by Heurico 1.16 in 71.3 seconds.