The generator matrix 1 0 0 1 1 1 X 1 1 X+2 1 1 X X+2 X X+2 1 1 0 1 1 X+2 1 1 2 0 1 1 X 1 1 X 1 1 1 0 1 1 0 2 2 X 0 X 1 1 1 X 1 0 1 1 1 1 1 1 1 0 1 2 1 1 1 0 X X 1 1 1 X 2 1 1 1 1 1 X 0 1 0 X 1 X+3 1 X+2 0 2 1 X+1 X+2 1 1 1 X 3 1 0 X+1 1 X+2 X+1 X+2 1 X 1 1 1 1 X 1 0 2 1 X+1 X+1 1 1 1 1 1 2 2 2 X+3 X+2 X 2 0 X 3 X+1 X 3 X+1 1 3 1 0 3 2 1 X+2 1 2 X+1 X 1 X 2 3 2 X X+3 1 0 0 1 1 X+3 X+2 1 X+3 X+2 1 1 0 1 X+1 X 0 X+2 2 1 X+3 3 X+2 0 X+3 1 X+2 X+1 X 1 2 1 1 X X+2 3 1 0 2 X+3 X+3 2 3 X+2 1 3 1 X+3 1 0 1 0 1 2 X 3 X+1 X+1 X+2 X+2 X+1 1 2 X+1 X 1 X+1 X 1 0 X+1 1 X+2 3 3 1 X X 0 0 0 2 0 0 0 0 2 2 0 0 0 2 2 0 2 0 2 2 2 2 2 0 0 0 2 2 2 2 2 2 2 0 2 2 2 0 0 2 2 2 0 2 0 2 2 0 2 2 0 2 2 2 2 2 0 0 2 2 0 2 2 0 0 2 2 2 0 2 0 0 0 0 2 0 2 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 2 0 2 0 0 0 2 2 2 2 0 2 0 0 2 0 0 2 2 0 2 2 2 2 0 0 2 0 2 0 0 0 2 0 2 0 0 2 2 2 2 0 0 0 0 0 2 2 0 2 0 2 2 0 0 2 2 0 2 2 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 0 2 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 2 0 2 0 2 0 2 2 0 0 0 2 2 0 2 2 2 0 2 2 2 2 2 0 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 0 2 2 2 0 0 2 2 2 2 0 0 2 2 2 0 2 2 0 2 2 2 2 0 0 2 2 2 0 2 2 2 2 0 0 0 0 2 2 2 0 2 0 0 0 2 0 0 0 2 0 0 2 2 2 2 2 0 2 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 2 0 0 0 0 0 2 2 2 0 0 2 2 0 0 0 0 0 2 2 0 2 2 2 2 2 2 2 0 0 2 0 2 2 2 2 2 2 0 0 0 2 2 0 2 0 2 2 0 2 2 0 2 0 0 0 2 2 2 0 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+256x^68+144x^69+652x^70+516x^71+1276x^72+916x^73+1440x^74+972x^75+1564x^76+1108x^77+1574x^78+1044x^79+1541x^80+732x^81+1016x^82+484x^83+480x^84+172x^85+264x^86+56x^87+103x^88+40x^90+20x^92+6x^94+6x^96+1x^104 The gray image is a code over GF(2) with n=308, k=14 and d=136. This code was found by Heurico 1.16 in 16.9 seconds.