The generator matrix 1 0 1 1 1 0 1 1 0 1 1 2 1 X+2 1 0 1 X+2 1 1 1 1 X 1 1 1 X+2 1 X+2 X 1 1 X+2 1 1 1 1 X 1 1 1 1 X+2 1 1 2 1 1 2 1 1 1 1 0 X 1 1 1 X+2 X 1 1 1 X+2 1 1 1 1 1 1 X+2 1 1 0 2 1 1 1 1 0 1 1 0 1 1 2 X+1 1 0 X+1 1 X+2 1 X+3 1 3 1 X X X+1 3 1 X+1 2 2 1 X+2 1 1 X+1 2 1 X+1 X+2 0 1 1 X+3 X+2 1 X+3 1 X X+3 1 X+2 3 1 X+1 X+1 1 X 1 1 0 X+2 1 1 1 0 X+3 X+1 1 2 0 0 1 1 X 1 X X+3 1 1 3 X+3 0 2 0 0 X 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 2 2 2 2 2 2 X+2 X X+2 X X X+2 X+2 X+2 X+2 X+2 X 2 X X X X+2 X+2 X 2 X 0 0 2 2 X+2 2 X+2 0 X+2 X 0 X+2 X+2 2 X X+2 X X X 2 0 X+2 X+2 X+2 X 2 0 X+2 0 2 X X 0 0 0 0 0 0 X 0 0 0 0 0 X 0 2 0 X X+2 X 2 X+2 2 X X X+2 X+2 0 X+2 2 0 X X+2 X+2 2 X 2 X+2 0 X+2 0 X+2 X+2 X 2 X 2 2 2 X+2 X 2 2 X 2 X 0 X+2 X+2 2 0 X+2 0 X 0 X X X+2 0 X X X+2 X 2 X+2 0 2 X 0 X+2 X+2 0 0 0 0 0 0 X 0 2 X+2 X 2 2 X+2 X X X+2 2 0 2 X+2 X+2 2 0 X 0 0 0 X+2 X 2 X X X 2 X 0 X+2 X X 0 0 0 X+2 X+2 2 0 0 0 0 X 2 X+2 X X 2 0 2 X X 2 X+2 0 X X+2 X+2 X+2 X+2 0 X 2 0 X X X X 2 X 0 X 0 0 0 0 0 0 X X+2 X+2 X+2 X+2 X 0 X 2 X X 2 2 2 X+2 X 0 X+2 X+2 X+2 X+2 0 X+2 0 X+2 0 2 X X 2 0 X 2 X 2 X+2 2 X 2 2 0 2 X X 2 0 0 0 X X+2 2 2 0 X+2 0 X+2 X X+2 2 2 0 0 0 X+2 X+2 0 X X+2 0 2 0 2 X X+2 generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+51x^68+70x^69+181x^70+322x^71+498x^72+614x^73+754x^74+1126x^75+1184x^76+1292x^77+1486x^78+1440x^79+1439x^80+1298x^81+1181x^82+1112x^83+715x^84+506x^85+433x^86+234x^87+137x^88+90x^89+63x^90+42x^91+28x^92+28x^93+26x^94+12x^95+8x^96+6x^97+2x^98+2x^100+1x^102+1x^104+1x^110 The gray image is a code over GF(2) with n=316, k=14 and d=136. This code was found by Heurico 1.16 in 18.5 seconds.