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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 0 1 1 1 1 1 X 1 2 1 X 1 2 1 1 1 1 X 1 1 X X X 0 X 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 X 0 2 X+2 2 X+2 2 X 0 0 X+2 X 0 2 0 2 X+2 X+2 X X 0 0 X+2 X+2 0 X X+2 2 2 2 X X+2 2 2 X+2 X 0 X+2 X X+2 X X+2 2 X 2 0 2 2 2 0 X+2 0 0 X+2 2 0 X 0 0 0 X+2 0 X+2 X+2 X+2 2 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 0 2 2 0 2 0 2 0 0 0 2 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 2 0 0 2 0 0 0 2 2 2 2 0 2 0 0 2 0 2 2 0 2 2 0 2 2 2 2 2 0 0 2 0 2 2 0 0 0 0 2 0 0 0 0 0 0 2 2 0 2 0 2 0 2 0 0 0 0 2 2 0 2 0 2 0 2 2 0 0 2 0 2 0 2 0 2 2 0 0 2 0 2 2 0 0 0 0 0 2 2 2 2 2 0 0 0 2 2 2 2 2 0 2 0 0 2 0 0 0 2 2 2 0 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 0 2 0 2 0 0 2 2 2 2 2 0 0 0 2 2 0 0 0 2 2 2 0 2 2 2 2 0 2 0 0 2 2 2 0 2 2 0 2 2 0 2 2 0 2 2 2 2 0 2 0 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 0 0 2 0 2 0 0 0 0 0 2 2 2 2 2 0 0 2 2 0 0 2 2 2 0 0 2 0 2 2 2 2 0 0 0 2 2 0 2 0 2 0 2 2 2 0 2 2 0 0 2 2 0 0 0 0 0 2 0 2 2 2 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 0 0 2 0 0 0 2 0 2 0 2 2 0 2 2 0 2 0 0 2 0 2 0 2 0 2 2 0 2 2 2 0 0 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 2 0 2 0 0 2 0 0 0 2 0 2 0 0 2 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 0 0 0 0 2 2 0 2 0 0 0 0 2 2 0 0 2 2 0 0 0 2 2 0 2 0 0 0 2 0 2 2 2 2 0 0 0 2 0 0 2 0 2 2 2 2 2 0 2 0 0 2 2 2 2 2 2 0 2 0 0 2 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69. Homogenous weight enumerator: w(x)=1x^0+42x^69+27x^70+72x^71+64x^72+86x^73+66x^74+208x^75+66x^76+378x^77+90x^78+380x^79+73x^80+184x^81+43x^82+60x^83+34x^84+58x^85+17x^86+44x^87+13x^88+18x^89+10x^90+4x^91+4x^92+2x^93+2x^94+1x^98+1x^136 The gray image is a code over GF(2) with n=312, k=11 and d=138. This code was found by Heurico 1.16 in 2.46 seconds.