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 1 1 2 2 1 1 1 1 1 2 1 1 0 2 2 1 1 1 1 1 X 2 X 1 1 1 1 2 1 2 1 X+2 2 X+2 1 X+2 1 1 X 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 0 X+1 1 1 X 2 X+2 X 3 1 X+2 0 X 1 1 1 X+1 X+3 2 X+1 X 1 X+2 1 0 X+2 2 X+1 0 1 1 3 1 1 1 0 1 X+2 X 1 2 X+3 1 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 3 X+3 X 1 1 X X+1 X+2 0 X+1 1 0 3 X+3 X+1 X 0 X+2 1 X+1 1 X+1 1 X+3 2 0 X+3 2 1 1 3 3 X+2 1 1 X 0 X+2 X+2 0 2 X+3 1 3 0 0 0 2 0 0 0 0 2 2 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 2 0 2 2 0 0 2 0 2 0 0 0 2 0 2 0 2 2 2 0 0 0 0 2 0 2 0 0 0 2 0 2 2 2 0 2 2 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 2 0 2 0 0 0 2 0 2 2 2 2 0 0 0 0 0 0 2 2 2 2 0 2 2 2 0 0 0 0 0 2 2 2 2 0 0 2 0 2 0 0 2 0 0 0 0 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 2 2 2 2 2 0 2 2 2 2 2 0 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 0 0 0 0 0 2 2 2 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 2 2 2 2 0 0 0 2 0 2 2 2 2 0 2 2 0 0 0 0 0 0 0 0 0 2 0 2 2 0 2 0 2 2 2 0 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 2 0 0 0 0 0 2 2 2 2 2 0 2 0 0 2 2 2 0 0 2 0 2 2 0 2 2 0 2 2 0 0 0 2 0 0 2 0 2 2 0 0 2 0 0 0 2 0 2 2 2 0 generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+114x^58+224x^59+481x^60+652x^61+981x^62+1016x^63+1217x^64+1364x^65+1331x^66+1596x^67+1488x^68+1484x^69+1165x^70+1068x^71+735x^72+572x^73+430x^74+180x^75+127x^76+24x^77+61x^78+12x^79+38x^80+13x^82+8x^84+1x^86+1x^88 The gray image is a code over GF(2) with n=268, k=14 and d=116. This code was found by Heurico 1.16 in 13.7 seconds.