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 X 0 X 2 1 1 X 2 X 1 0 1 1 X 1 X X X 2 0 1 1 1 1 1 1 2 X 1 1 0 1 X 1 0 2 1 0 1 1 0 X 0 X 0 0 X X+2 0 2 X 0 X+2 2 X+2 X X+2 0 X 0 X 2 0 X 0 2 X X+2 X X X X+2 0 X X X+2 X X 2 X+2 X+2 0 X+2 X+2 X X X X 2 0 2 2 X+2 X X 2 2 X X+2 X X 0 2 0 2 2 0 0 0 X X 0 X+2 X 0 0 X X 2 2 X+2 X 2 0 0 X 0 X X X+2 0 2 X 0 0 0 X X+2 2 0 X+2 X 0 X+2 2 X+2 X+2 0 X+2 2 X 2 X 2 X+2 2 0 0 2 X X+2 0 2 X X+2 X+2 2 X+2 X X X+2 X 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 2 2 2 2 2 0 2 0 0 0 2 2 0 2 2 0 2 2 2 0 2 2 0 0 0 2 0 2 2 0 0 0 2 2 0 0 0 0 2 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 0 2 2 2 2 2 0 2 0 0 0 2 2 0 0 2 2 0 0 0 2 2 0 0 2 2 0 2 0 2 2 2 2 2 0 2 2 2 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 2 2 0 2 2 0 2 2 2 0 0 0 0 2 2 0 2 0 0 2 2 0 2 0 2 2 0 2 0 0 2 0 2 2 2 2 2 2 0 2 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 0 0 2 2 0 2 0 2 2 0 2 2 0 0 0 2 2 0 0 2 0 2 2 0 0 2 2 0 0 2 2 0 2 2 2 0 2 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 2 0 0 2 2 0 2 0 0 0 2 2 2 0 2 0 2 2 0 2 2 2 0 2 0 0 0 0 0 2 0 2 0 2 2 0 2 0 2 0 2 0 2 0 2 2 2 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 2 0 0 0 2 0 2 0 2 2 0 0 2 0 2 2 0 0 0 0 0 2 2 2 0 2 0 0 2 2 2 0 2 0 2 0 2 0 0 2 2 2 2 2 0 0 0 0 generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+73x^56+241x^58+24x^59+451x^60+64x^61+652x^62+224x^63+787x^64+448x^65+950x^66+528x^67+887x^68+448x^69+761x^70+224x^71+605x^72+64x^73+357x^74+24x^75+206x^76+86x^78+50x^80+20x^82+7x^84+5x^86+4x^88+1x^92 The gray image is a code over GF(2) with n=268, k=13 and d=112. This code was found by Heurico 1.16 in 6.26 seconds.