The generator matrix 1 0 0 1 1 1 X+2 1 1 X 1 2 1 2 1 1 X 1 X 1 X 1 1 1 X+2 X 1 X 1 X+2 2 1 1 1 1 1 X+2 1 1 1 1 X+2 1 X X+2 X 1 1 1 X 1 X 1 0 2 X+2 1 2 1 2 1 2 1 1 1 1 0 X 1 1 1 2 2 1 0 1 2 1 0 1 0 0 1 X+3 1 X+2 X+3 1 3 1 X X X 0 X 3 1 1 1 X+2 0 3 0 1 3 0 2 1 1 X X+3 X+3 3 2 1 0 X X+3 3 X+2 0 1 1 1 1 2 X+2 1 X+1 1 X+3 1 1 1 X 1 X+3 1 1 0 3 X X X 1 1 3 X+3 2 1 1 X+2 1 0 X 0 0 0 1 1 X+1 0 X+3 1 X+3 X+2 X 3 X 1 X+1 X+2 1 1 1 0 2 0 X+3 X+2 1 X+1 X+3 1 X+2 X+2 X+2 X+1 X X+3 X 2 3 X+3 X+3 1 X+1 1 1 X+3 X+1 0 1 3 3 0 2 X X+3 X+1 2 X 1 1 X+2 1 0 1 1 0 X+2 2 1 X+3 1 X+3 2 1 3 2 X 2 X+2 0 0 0 0 X X X+2 0 X+2 X+2 0 X+2 2 2 0 X 2 2 X 2 X+2 2 0 X+2 X+2 0 X 2 X 0 X X+2 0 0 2 2 X+2 X+2 X+2 2 X X+2 X 0 2 X 0 0 2 2 X+2 X+2 0 2 0 X+2 2 2 X+2 2 2 X+2 X+2 2 X+2 X X X+2 X 2 0 0 X X 0 2 2 X+2 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 2 2 0 2 2 2 2 2 2 0 0 0 0 2 2 0 2 0 2 2 0 2 2 0 2 2 2 2 2 2 0 2 0 2 0 2 2 0 2 0 2 2 2 0 2 0 0 2 0 0 2 2 0 0 0 0 0 0 0 2 0 2 2 2 0 2 2 2 2 0 2 2 0 0 2 0 2 2 0 2 0 0 0 0 0 0 2 0 0 0 2 2 0 2 0 0 2 2 0 2 0 2 0 2 0 0 2 2 2 2 0 0 0 0 2 0 0 2 0 0 2 0 2 0 0 2 2 2 0 2 2 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 0 2 0 0 0 0 2 0 2 2 0 0 2 2 2 0 2 2 2 2 2 0 0 0 0 2 0 2 0 0 0 2 0 2 2 0 0 0 2 0 0 2 2 0 0 0 2 0 2 0 2 0 2 2 0 2 2 0 2 2 2 0 2 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+61x^68+166x^69+355x^70+522x^71+713x^72+878x^73+1077x^74+1162x^75+1284x^76+1416x^77+1280x^78+1414x^79+1294x^80+1226x^81+1119x^82+684x^83+606x^84+458x^85+206x^86+158x^87+96x^88+70x^89+46x^90+26x^91+35x^92+8x^93+11x^94+2x^95+4x^96+2x^97+2x^98+2x^100 The gray image is a code over GF(2) with n=312, k=14 and d=136. This code was found by Heurico 1.16 in 15.7 seconds.