The generator matrix 1 0 0 0 0 1 1 1 1 1 1 1 2 X X 0 0 X+2 1 0 1 1 2 1 X 2 1 X 1 1 1 1 X 1 0 0 2 1 X 1 1 1 0 1 1 0 X X+2 2 X+2 2 X+2 1 1 2 1 0 0 1 1 2 X+2 X+2 2 X 1 X X+2 1 X 0 1 1 X+2 2 1 1 2 2 1 0 1 0 0 0 0 2 2 0 3 X+3 X+1 1 1 1 X+2 X 1 2 1 X X+2 1 X+1 1 0 X+3 X 3 X+3 3 X+1 1 X+2 X 2 1 X+2 2 2 X+2 1 1 3 X 2 1 1 1 X+2 1 1 X+1 X+2 1 1 1 0 X+1 X+2 2 2 1 X+2 X 2 2 1 X+2 1 1 3 2 1 2 X+1 0 1 1 0 0 0 1 0 0 0 3 X+1 1 1 2 X+3 1 X+1 X 1 1 1 X+2 X+1 3 X+2 X 1 2 1 0 X X 2 X+3 X 2 2 0 0 X+1 X+2 1 X+3 X 1 X+2 X 3 1 2 X+1 X+2 2 3 3 3 X+1 3 0 0 2 0 X+2 2 1 X+2 1 1 0 1 0 3 X+2 X+1 2 X+3 X 1 X+1 2 X+3 0 X+2 0 0 0 1 0 1 1 X X X+2 X+2 3 1 X+1 1 X X+3 2 3 X 3 2 X+2 X+1 3 X+3 X+1 1 2 1 X+2 X+3 X+2 0 1 1 2 0 X X+3 X+3 X+3 X+1 3 X+2 3 1 X+2 X X 1 X+3 1 X+3 1 0 X+2 1 X+2 X+2 1 3 2 X+2 X+3 X+1 X 2 2 3 2 X+1 0 X 0 2 0 3 3 0 0 0 0 0 1 1 2 0 X+1 2 0 1 1 0 3 X+3 X+2 3 X+2 X+2 X+1 3 X+1 0 X X+3 1 X+1 1 X 1 0 1 3 X X+1 2 X 3 X+2 2 2 X 3 X+2 2 1 X+3 X+1 1 1 X X+1 X+3 X+2 2 X 1 3 2 X+1 X+1 X+3 X+2 X X+1 X+3 0 X+3 X+2 X+3 X 3 0 X+3 X+3 X+1 2 X+3 X+2 0 0 0 0 0 X 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 X X+2 X X X+2 X X+2 X X X+2 X+2 X X+2 X+2 X X+2 X+2 X+2 X+2 X X X+2 X X X+2 X X+2 X X 2 X+2 0 X+2 2 X X X 2 X 0 0 generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+117x^68+584x^69+1039x^70+1984x^71+2652x^72+4002x^73+4658x^74+6648x^75+7187x^76+9548x^77+9477x^78+12002x^79+10719x^80+11918x^81+9922x^82+9906x^83+7659x^84+6912x^85+4537x^86+3730x^87+2296x^88+1596x^89+834x^90+560x^91+259x^92+180x^93+59x^94+44x^95+20x^96+10x^97+2x^98+4x^99+2x^100+2x^105+2x^107 The gray image is a code over GF(2) with n=320, k=17 and d=136. This code was found by Heurico 1.13 in 283 seconds.