The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 X+2 1 1 0 1 0 1 1 1 1 X+2 1 0 X+2 1 1 1 1 1 X 1 0 1 1 X+2 0 1 1 1 1 1 1 1 1 1 X+2 0 0 1 1 1 1 2 1 1 1 2 2 0 1 0 X 2 0 0 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 X+2 1 X+1 0 1 3 1 X+1 0 X+2 3 1 X+1 1 1 3 0 X+1 3 X+2 1 0 1 X+2 0 1 1 X+2 0 X+1 3 X+2 0 X+1 X X+2 1 1 1 3 3 0 X+2 1 1 3 2 1 1 1 X 1 0 1 1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 2 0 2 0 2 2 0 2 2 0 0 2 2 0 0 2 2 2 2 2 0 0 2 2 0 0 0 0 2 2 0 0 2 0 2 2 0 2 2 0 2 2 0 2 2 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 0 2 2 2 0 2 2 2 0 0 0 0 0 2 2 2 0 0 0 2 2 2 2 2 2 2 2 2 2 0 2 2 2 0 0 0 2 0 0 2 0 0 2 2 2 2 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 2 2 0 2 0 2 2 0 2 2 0 0 0 2 0 2 0 2 0 2 2 2 0 2 2 2 0 0 0 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 2 0 0 0 0 2 2 0 2 2 0 2 0 0 2 2 2 0 2 2 0 0 2 2 2 0 2 0 0 0 0 2 2 2 2 2 0 2 2 0 2 0 2 0 0 2 0 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0 2 0 2 0 2 2 0 0 2 2 0 2 0 0 2 0 0 2 0 2 2 0 0 0 2 0 2 0 0 2 2 2 0 0 0 2 0 2 2 0 2 0 0 0 2 0 2 2 2 0 2 2 2 2 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 0 2 2 0 0 0 2 2 2 2 0 0 0 0 2 2 2 2 0 2 2 2 0 2 0 2 2 2 0 2 2 2 2 0 2 2 0 0 0 2 2 2 0 0 0 2 2 2 2 2 2 0 2 2 2 2 0 0 0 0 0 0 0 0 2 0 2 2 0 2 2 0 0 2 0 0 2 2 2 2 0 2 2 0 2 0 0 2 2 0 2 2 0 0 0 2 0 0 2 0 0 2 0 0 0 2 0 2 0 0 2 2 2 0 0 2 2 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 2 2 0 2 0 2 2 0 0 2 0 2 0 2 2 0 2 0 2 0 0 0 2 0 2 2 2 2 2 0 0 0 0 0 0 0 2 2 0 2 2 2 2 2 0 0 0 2 0 2 2 0 0 2 0 0 2 2 0 generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56. Homogenous weight enumerator: w(x)=1x^0+84x^56+16x^57+76x^58+72x^59+403x^60+224x^61+530x^62+528x^63+1281x^64+960x^65+1664x^66+1296x^67+2199x^68+1248x^69+1756x^70+928x^71+1203x^72+560x^73+516x^74+232x^75+305x^76+64x^77+66x^78+16x^79+93x^80+53x^84+9x^88+1x^96 The gray image is a code over GF(2) with n=272, k=14 and d=112. This code was found by Heurico 1.16 in 15.8 seconds.