The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 0 2 0 0 0 0 2 2 2 2a 2a 2a+2 0 0 2 2a 2a 2 2 0 2 2a 2 2a 2 0 0 0 0 2 0 0 2 2a+2 2a 2a+2 0 2a+2 0 2a 2 2 2a+2 2a 0 2a 2 2a 2a 2 2 0 0 0 0 0 0 2 0 2a+2 0 2 2a+2 2a 2a+2 2a 2a+2 2a+2 2a+2 0 2a 2a 2 2 2a+2 2a 2a 2a+2 2a+2 0 2 0 0 0 0 2 2 2 2a+2 2a+2 2a+2 2a 2 2a+2 2a+2 2a+2 2a+2 2a 0 0 0 2 2a+2 2 0 2a 2a+2 2a generates a code of length 27 over GR(16,4) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+72x^68+195x^72+165x^76+768x^78+159x^80+2304x^82+123x^84+129x^88+99x^92+48x^96+21x^100+12x^104 The gray image is a code over GF(4) with n=108, k=6 and d=68. This code was found by Heurico 1.16 in 0.0657 seconds.