The generator matrix 1 0 1 1 1 X+2 1 1 0 X+2 1 1 1 2 1 X+2 1 1 1 X 1 2 1 1 1 1 1 2 1 X 1 1 1 1 X+2 1 2 1 1 0 2 1 1 1 1 1 0 1 1 2 0 1 X+2 1 1 1 X+2 1 1 1 2 0 1 1 1 1 1 1 1 X+2 1 1 X 2 X 1 X+2 1 0 1 1 0 X+3 1 X X+1 1 1 X+2 3 2 1 1 1 1 X X+1 1 X+2 1 0 X+1 X+1 0 1 1 X+1 1 0 2 0 3 1 X 1 3 X+2 1 1 X+2 1 X+3 2 2 1 X+1 0 1 1 2 1 3 1 X 1 3 2 0 1 1 1 X+3 X+3 0 X+3 2 1 1 X+2 X+1 0 1 2 1 1 X 0 0 X 0 X+2 0 0 X X+2 X 2 X X X 0 2 2 X 0 X X 2 X 2 X 0 2 2 0 X+2 0 X+2 0 X+2 2 X X+2 X 0 0 X 0 2 0 X+2 0 0 X+2 X+2 X X+2 0 X+2 X+2 X+2 X 0 X X 0 2 2 0 X+2 2 2 X+2 X 0 X+2 X+2 X X 0 X+2 X+2 X X 0 0 0 X 0 0 X X X X 0 X 0 2 X+2 X+2 0 2 X+2 2 X+2 X X 2 X 0 X X+2 0 X X+2 2 2 0 X X+2 2 X+2 X 0 X+2 2 X X X+2 2 X+2 0 X 0 0 X+2 X+2 X 0 X+2 2 X 0 0 X+2 0 2 0 X+2 0 X+2 2 X+2 2 X+2 2 X 0 X+2 0 X+2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 0 2 2 0 0 2 2 2 2 2 0 2 2 2 2 0 0 2 2 0 0 2 0 2 2 2 0 0 0 0 0 2 0 2 0 2 0 0 2 0 0 2 0 2 0 2 2 0 2 0 0 0 0 0 2 2 0 0 0 0 0 2 0 0 0 2 2 0 2 2 0 0 0 0 0 0 2 2 2 0 0 2 2 0 2 0 0 2 0 2 2 2 0 2 2 2 0 2 0 2 0 2 0 0 0 0 2 0 0 2 2 2 0 2 2 0 0 2 2 2 0 2 0 2 2 0 0 2 2 2 0 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 0 2 0 2 2 2 2 2 0 2 2 0 2 2 0 2 0 2 0 0 0 0 0 0 0 2 2 2 0 2 0 0 2 2 0 0 2 0 2 2 0 2 0 2 0 0 2 0 0 2 2 2 0 0 0 0 2 2 2 0 0 0 0 2 0 0 2 0 2 2 2 0 0 2 2 2 0 2 2 2 0 0 2 0 2 2 2 2 2 0 0 0 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+208x^68+24x^69+566x^70+248x^71+968x^72+320x^73+1444x^74+644x^75+2007x^76+796x^77+2092x^78+820x^79+1988x^80+684x^81+1386x^82+300x^83+837x^84+220x^85+416x^86+36x^87+199x^88+4x^89+90x^90+47x^92+22x^94+11x^96+5x^100+1x^104 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 45.4 seconds.