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 X 0 1 X 0 1 1 1 X 1 1 1 0 1 1 1 1 1 X 0 1 1 0 1 0 1 X 1 X 1 1 1 1 0 1 X X X 1 0 1 X 1 1 0 X 0 X+2 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 X 0 2 0 0 2 X+2 X+2 X+2 X+2 X X X+2 X X+2 X X+2 X+2 2 2 X X X X+2 0 0 2 X+2 X X X+2 X 0 X X+2 X+2 2 X+2 0 2 2 X+2 X 0 X+2 X+2 X 2 X X+2 X+2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 2 0 2 0 2 0 0 0 2 0 2 0 2 0 0 2 0 2 2 0 2 0 2 0 0 2 2 2 0 0 2 0 2 2 2 0 0 0 0 2 2 2 0 0 2 2 2 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 0 0 0 0 0 0 2 2 2 0 0 0 2 2 2 0 0 0 0 0 2 0 2 2 2 2 2 2 2 0 0 2 0 2 0 2 2 2 0 2 2 0 0 0 2 2 2 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 0 0 0 2 0 0 0 2 2 2 2 0 2 2 0 0 0 2 0 2 2 0 2 2 2 0 2 2 2 0 0 2 0 2 0 2 2 2 2 0 0 2 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 0 2 0 0 2 0 0 2 2 2 0 2 0 0 2 0 2 2 0 2 0 2 2 0 0 2 0 2 0 0 2 0 2 0 2 2 2 0 0 0 2 2 0 0 0 0 2 2 2 0 2 2 2 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 0 2 2 2 2 0 0 0 2 2 0 2 0 2 0 2 2 2 2 2 0 2 2 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 2 2 2 2 2 0 0 2 2 0 2 2 0 0 0 0 2 0 2 0 0 0 0 2 0 2 0 2 2 2 0 0 0 0 0 2 2 0 2 0 2 2 0 2 2 2 0 0 2 0 2 2 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 0 2 2 2 0 2 0 2 2 2 0 0 0 2 0 0 0 0 2 0 0 2 2 0 0 0 0 2 2 0 2 0 2 2 2 0 2 2 0 0 2 2 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+12x^56+12x^57+77x^58+92x^59+100x^60+180x^61+126x^62+320x^63+116x^64+576x^65+124x^66+712x^67+109x^68+576x^69+91x^70+320x^71+93x^72+180x^73+56x^74+92x^75+51x^76+12x^77+20x^78+15x^80+13x^82+11x^84+3x^86+3x^88+1x^90+1x^92+1x^98 The gray image is a code over GF(2) with n=268, k=12 and d=112. This code was found by Heurico 1.16 in 1.6 seconds.