The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 2a+2 1 1 2a+2 0 1 2a+2 1 1 2a+2 1 1 0 1 0 0 0 2a+2 1 3a+2 3a+3 1 2a+3 a+1 3a+3 a a 1 3a 2a+3 1 1 1 1 2 2a+2 1 3 2a+2 0 0 1 1 a 3a+3 1 3 1 3a+3 0 a 3a+3 0 a+2 2a+1 a+1 a 3a+1 a 2 2a+2 2 a+3 1 2a+3 a+1 0 0 0 2a+2 0 0 0 2 2 2 2a 2a 2a+2 2a 2a+2 2a 2a 2a 2a+2 2 2a+2 0 2 2 0 2a+2 2a 0 0 0 0 2 2a+2 2a 2 2a+2 2a 2a 2a+2 2a 2 2a 2a 2a+2 0 0 0 0 2a+2 2a+2 0 2 2a+2 0 generates a code of length 27 over GR(16,4) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+282x^68+456x^69+168x^70+756x^71+1467x^72+1776x^73+768x^74+1728x^75+3060x^76+4320x^77+2448x^78+4680x^79+5940x^80+7152x^81+3648x^82+5472x^83+6003x^84+6360x^85+2184x^86+2724x^87+2517x^88+1440x^89+90x^92+69x^96+21x^100+6x^104 The gray image is a code over GF(4) with n=108, k=8 and d=68. This code was found by Heurico 1.16 in 6.38 seconds.