The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 1 1 1 X X X 1 0 1 2 2 X 1 2 1 X X 1 1 1 1 0 2 1 0 X 0 1 1 1 X 2 1 1 1 X X 1 X 1 0 2 1 1 1 1 0 X 0 X 0 0 X X+2 0 2 X 0 X+2 2 X+2 X X+2 0 X 0 X 2 0 X X 0 X+2 X 2 X 2 0 0 X X+2 0 X X+2 2 X X X X X 2 X 0 X X 0 2 0 2 X X X+2 X 0 X X 2 2 X X X 2 0 X+2 0 2 0 X+2 0 X X X 2 0 0 0 X X 0 X+2 X 0 0 X X 2 2 X+2 X 2 0 0 X 0 X X X+2 0 X+2 X+2 X 0 X 2 X X X+2 X+2 X+2 X+2 X 0 0 2 X+2 X X X 0 X+2 X+2 2 X+2 0 2 0 X 2 X X X+2 X X 0 X X+2 2 0 X 2 X 0 X X X 0 X X+2 0 X X 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 0 2 2 2 2 2 0 0 2 0 2 2 2 2 0 2 2 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 0 0 2 2 2 2 0 2 0 0 2 2 0 0 0 2 2 2 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 2 0 0 2 2 0 2 2 0 0 2 0 2 2 0 2 2 0 2 2 0 2 2 2 0 2 2 0 0 0 0 2 0 0 0 2 0 0 2 0 2 0 2 0 0 2 0 2 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 0 2 0 2 2 2 0 0 0 0 2 0 2 2 2 2 2 0 2 2 0 2 0 2 0 2 2 0 2 2 2 2 2 0 2 0 2 2 2 0 0 0 2 0 0 0 2 0 2 0 2 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 2 2 0 2 0 2 0 0 2 2 0 2 0 2 2 2 2 0 2 0 0 2 0 0 2 2 2 2 0 2 0 0 0 0 0 2 2 0 2 0 2 0 2 2 0 2 2 2 2 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 2 0 0 2 2 0 2 0 2 2 2 2 2 0 0 2 2 0 0 0 0 2 0 2 2 0 2 2 0 0 2 0 2 0 0 2 0 2 0 0 2 0 2 2 0 2 2 0 0 0 2 2 0 2 0 0 0 2 2 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 0 2 2 2 2 0 0 2 2 2 2 0 0 2 2 2 0 2 0 2 0 2 2 2 2 0 0 0 0 2 0 2 0 2 2 2 2 0 0 0 2 2 0 0 2 2 2 0 0 0 2 0 0 2 0 0 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+34x^66+62x^67+100x^68+122x^69+212x^70+282x^71+358x^72+344x^73+451x^74+540x^75+571x^76+708x^77+676x^78+714x^79+615x^80+596x^81+459x^82+306x^83+283x^84+214x^85+154x^86+90x^87+86x^88+52x^89+45x^90+52x^91+18x^92+12x^93+12x^94+2x^95+10x^96+3x^98+3x^100+2x^102+2x^104+1x^108 The gray image is a code over GF(2) with n=312, k=13 and d=132. This code was found by Heurico 1.16 in 7.45 seconds.