The generator matrix 1 0 0 1 1 1 0 1 1 2 1 X 1 X+2 1 X+2 1 1 1 2 X 2 0 1 2 1 1 1 1 1 X+2 1 1 X 1 2 X 1 1 X 2 1 1 2 X 1 2 0 2 X 1 1 1 X+2 1 1 2 1 1 0 1 X+2 X+2 1 1 1 1 0 1 1 0 X+2 1 X+2 X+2 1 1 2 1 0 1 1 1 1 1 0 1 0 0 1 1 1 2 1 1 X+1 X+2 X 1 X+2 1 X+3 X+1 X+2 X+2 1 2 1 1 1 3 2 X+2 X+2 X+3 0 0 X+1 1 X+3 1 1 2 0 1 1 X 3 1 0 X X+2 1 X 1 X+3 X+2 2 X+2 X+2 0 1 3 X+3 1 2 1 1 X+3 X+3 1 2 1 X+1 X+3 1 1 2 1 1 2 X+3 X+2 0 1 X+2 X+3 X 1 3 0 0 1 X+1 X+3 0 X+1 X 1 X 0 1 1 1 X 2 X+2 X+1 X+1 1 X+3 1 X+2 X+1 1 0 X+1 0 2 3 1 3 X+2 2 2 2 3 2 0 X 1 3 X+2 3 1 X+2 1 X+2 1 X+1 X+1 X+3 X+1 1 3 X+3 X X+1 3 X+1 X X+2 X+1 3 2 X X+2 X+3 X+1 X+3 X+2 2 0 2 2 1 X 1 X+1 1 1 1 2 0 X+2 0 0 0 2 0 0 0 2 2 0 2 2 0 2 0 2 2 0 2 2 0 0 2 2 2 0 0 0 0 0 2 0 2 0 0 2 2 2 0 0 2 2 0 0 0 2 2 0 2 0 2 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 0 2 0 2 2 0 0 2 2 2 0 0 0 0 2 2 0 0 2 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 0 2 0 2 0 2 2 2 2 2 2 0 0 2 0 0 2 0 2 0 0 0 0 2 2 2 0 0 2 0 0 0 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 0 2 2 2 2 0 0 2 2 0 0 2 2 0 0 2 0 2 2 0 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 2 2 0 2 2 0 0 2 2 2 2 2 2 0 2 2 0 0 2 2 0 2 2 2 0 0 2 0 2 0 0 2 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 2 2 0 0 2 0 2 0 2 0 2 2 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 2 0 2 2 0 0 2 0 0 2 2 0 2 0 0 2 0 0 2 2 0 2 2 2 0 2 2 0 0 0 0 2 0 0 2 2 0 0 0 2 2 2 2 2 0 0 0 0 0 0 2 0 0 2 2 0 2 2 0 2 2 2 0 0 2 0 0 2 2 0 generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+178x^77+247x^78+536x^79+372x^80+712x^81+518x^82+844x^83+497x^84+896x^85+435x^86+698x^87+426x^88+502x^89+259x^90+374x^91+198x^92+226x^93+59x^94+94x^95+27x^96+40x^97+14x^98+14x^99+9x^100+4x^101+3x^102+6x^104+2x^105+1x^106 The gray image is a code over GF(2) with n=340, k=13 and d=154. This code was found by Heurico 1.16 in 19.1 seconds.