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 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X X^2+2 X 0 X X^2+2 X 1 1 X^2 1 0 X X^2+2 X^2+X 0 X^2+X X^2+2 X+2 0 X^2+X X+2 X^2+2 0 X^2+X X^2+2 X 0 X^2+X X^2+2 X+2 0 X^2+X X^2+2 X 0 X^2+X X^2+2 X 0 X^2+X X^2+2 X+2 2 X^2+X+2 X^2 X+2 2 X^2+X+2 X^2 X 2 X^2+X+2 X^2 X 2 X^2+X+2 X^2 X+2 2 X^2+X+2 X^2 X+2 2 X^2+X+2 X^2 X 2 X^2+X+2 X^2 X 2 X^2+X+2 X^2 X+2 X^2+X X X+2 X X^2+X X X+2 X 0 X^2+X X+2 0 X^2+X 0 0 2 0 0 0 2 0 0 2 2 2 0 2 2 2 2 0 0 2 2 2 0 0 2 0 0 2 2 2 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 0 0 0 2 0 0 0 0 2 0 0 0 2 2 2 2 2 2 0 2 0 2 0 0 2 2 2 0 0 0 2 2 0 0 0 2 2 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 0 2 0 0 2 2 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 0 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 0 2 2 0 0 0 0 2 2 2 2 0 0 0 0 2 2 0 2 2 0 0 2 2 0 0 0 2 0 2 generates a code of length 77 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+58x^74+200x^75+44x^76+384x^77+122x^78+176x^79+19x^80+10x^82+8x^83+1x^86+1x^134 The gray image is a code over GF(2) with n=616, k=10 and d=296. This code was found by Heurico 1.16 in 0.485 seconds.