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 0 1 X 1 2 1 1 1 1 X 1 0 1 1 X 1 1 1 1 1 1 X 1 X 1 1 X 1 X X X X 1 X 1 1 X 0 X 1 1 0 X 0 X 0 X 0 0 X X+2 0 2 X+2 X 0 X X 2 2 0 X X+2 0 0 X+2 X+2 2 X+2 X 2 2 X X 0 X+2 0 X 0 2 X X X 2 X+2 0 X+2 2 2 X X X X+2 2 0 2 2 0 2 0 0 X 0 X+2 2 X+2 X+2 0 X 2 2 2 X X+2 2 X X+2 2 0 2 0 0 X X 0 X+2 X 0 2 X 0 X 0 X+2 2 X+2 X 0 X 2 X+2 0 2 X 2 X 2 0 X X+2 2 X+2 0 X 0 X+2 X 0 X+2 X+2 0 X X+2 2 2 X 0 X X X+2 X X+2 X+2 X+2 X+2 X X+2 X+2 2 0 2 X+2 X+2 2 X+2 0 0 X X+2 2 0 X X+2 X+2 X X X 0 0 0 2 0 0 0 0 2 2 2 0 2 2 2 2 2 0 2 2 2 2 2 2 2 2 0 0 2 2 0 0 2 2 2 0 0 2 2 2 0 2 0 0 0 0 0 0 0 2 2 2 0 0 2 2 2 0 0 2 2 2 2 2 2 0 2 0 0 0 2 2 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 2 2 0 0 0 0 2 2 2 2 2 0 2 0 2 0 2 2 0 0 0 2 0 2 2 2 0 2 0 0 0 0 0 2 2 2 0 0 2 2 2 0 0 2 0 2 2 2 2 2 2 0 0 0 0 2 0 2 2 0 0 2 0 0 2 0 0 0 0 0 2 0 0 0 2 0 2 2 0 2 0 2 0 0 2 2 0 0 0 0 2 2 2 2 0 0 2 0 2 2 0 0 2 2 2 0 0 0 0 2 2 0 2 2 2 0 2 2 0 0 2 0 0 2 0 2 0 0 0 2 2 0 0 2 0 0 2 0 0 2 2 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 2 0 2 2 0 2 0 0 2 0 2 2 2 2 2 2 0 0 0 0 0 0 2 0 2 0 2 0 0 0 2 0 0 2 0 0 0 0 2 0 2 2 2 2 2 0 0 2 2 0 0 0 2 2 0 0 2 2 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 0 0 2 0 2 0 0 2 0 2 2 0 0 2 2 0 2 2 0 2 2 2 0 2 2 2 2 2 0 2 2 2 2 0 2 2 2 2 2 2 0 2 0 2 0 2 0 2 2 2 2 0 2 0 0 0 0 0 2 2 0 2 generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+130x^68+20x^69+208x^70+68x^71+397x^72+128x^73+406x^74+192x^75+487x^76+216x^77+440x^78+184x^79+388x^80+128x^81+242x^82+64x^83+154x^84+20x^85+78x^86+4x^87+80x^88+32x^90+19x^92+2x^94+5x^96+1x^100+1x^104+1x^116 The gray image is a code over GF(2) with n=308, k=12 and d=136. This code was found by Heurico 1.16 in 1.84 seconds.