The generator matrix
1 0 0 1 1 1 1
0 1 0 1 a 0 0
0 0 1 3a+3 a 0 0
0 0 0 2 0 2 0
0 0 0 0 2 2 0
generates a code of length 7 over GR(16,4) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+30x^8+192x^9+267x^12+1152x^13+1152x^15+741x^16+2304x^17+3072x^18+6912x^19+846x^20+21888x^21+9216x^22+10368x^23+2028x^24+5184x^25+183x^28
The gray image is a code over GF(4) with n=28, k=8 and d=8.
This code was found by Heurico 1.16 in 0.292 seconds.