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 X 1 X 1 1 X X 1 1 2 2 1 1 X 1 1 1 X 1 1 1 1 1 0 1 X 0 1 0 2 X 2 0 1 1 1 0 2 X 1 0 X 0 X 0 0 X X+2 0 2 X+2 X 0 X X 0 2 X X+2 2 0 2 X 2 X 0 2 X X+2 0 X+2 X+2 2 2 X+2 0 X 0 X X+2 2 X+2 2 0 X+2 2 X X X 0 X X X+2 0 2 X+2 0 2 X X X 2 X 2 0 2 X X 2 2 X 2 2 X+2 0 X 2 0 0 0 X X 0 X+2 X 0 2 X 0 X 0 X+2 2 X+2 X X 2 2 2 X 0 2 X+2 0 X+2 0 0 X+2 X X 2 X 0 0 X X+2 X+2 0 X X+2 X+2 X+2 2 2 X X+2 X+2 X+2 X X+2 0 X 0 0 X X+2 X+2 2 0 X X+2 X X 2 2 X X X X 2 X 2 X X X 0 0 0 0 2 0 0 0 0 2 2 2 0 2 0 2 0 0 2 2 0 2 0 0 0 2 2 0 0 2 2 2 0 0 2 0 0 0 0 0 2 2 2 0 0 0 2 2 0 2 0 2 2 2 2 0 0 0 2 0 2 0 2 2 0 2 0 0 0 2 2 2 0 2 2 2 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 0 2 2 0 2 0 2 0 2 0 2 0 2 0 0 2 0 2 0 0 0 2 2 0 2 0 2 0 2 2 2 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 2 2 2 0 2 0 0 0 0 2 2 0 0 2 2 0 2 0 2 0 0 2 2 2 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 0 0 0 0 2 0 2 2 2 0 0 2 0 2 2 2 2 2 2 2 2 0 2 2 0 0 0 0 0 0 0 2 0 2 2 2 2 2 2 2 0 0 0 2 0 2 0 0 0 0 2 0 0 2 2 0 2 0 2 2 2 0 2 2 0 0 2 2 0 2 0 2 2 0 2 2 2 0 0 2 0 2 2 0 0 0 0 2 2 2 2 2 0 0 2 2 2 0 2 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 2 2 0 0 2 2 2 2 0 2 0 2 0 2 0 0 0 2 0 2 0 2 2 2 0 2 2 0 2 2 2 0 2 2 0 2 0 2 2 2 0 2 0 0 0 2 0 2 0 0 0 2 2 2 2 2 0 2 0 2 2 2 2 generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+58x^68+90x^69+102x^70+84x^71+194x^72+118x^73+428x^74+114x^75+504x^76+112x^77+551x^78+130x^79+541x^80+110x^81+331x^82+110x^83+184x^84+60x^85+91x^86+50x^87+36x^88+20x^89+22x^90+24x^91+12x^92+2x^93+7x^94+4x^96+3x^98+2x^100+1x^118 The gray image is a code over GF(2) with n=312, k=12 and d=136. This code was found by Heurico 1.16 in 1.84 seconds.