The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 0 1 1 X+2 1 1 0 1 1 1 1 X+2 1 0 1 1 1 X+2 1 X+2 1 1 0 1 X+2 1 1 1 1 1 1 0 1 X X+2 1 1 1 X+2 1 1 1 1 X 1 1 1 1 X X X+2 1 1 1 1 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 1 0 3 1 X+2 X+1 1 X+1 0 3 X+2 1 X+1 1 2 X+2 3 1 0 1 3 X 1 X+1 1 0 3 X+1 X+3 X+2 3 1 0 1 1 0 X+2 3 1 1 X+1 X+1 X+3 1 X+3 X+2 1 X+1 1 1 1 X+1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 2 0 2 2 2 0 2 2 2 2 0 2 2 2 0 2 2 0 0 2 0 2 2 2 0 0 2 0 0 2 2 0 2 0 2 0 0 0 0 2 2 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 2 0 2 2 2 2 0 0 2 0 2 2 2 0 2 2 0 0 2 0 2 2 0 2 0 0 2 0 2 0 2 0 2 2 0 2 2 2 2 2 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 2 0 2 2 2 2 2 0 0 0 0 2 0 0 0 2 2 2 2 2 0 2 0 0 0 0 2 0 2 2 0 2 2 2 2 0 0 0 2 0 0 0 0 0 0 2 2 2 2 0 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 0 0 2 2 0 2 0 2 0 2 2 2 0 2 0 0 2 0 2 2 2 0 0 2 2 0 0 2 0 2 0 0 2 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 0 2 2 0 0 2 2 0 0 2 2 0 0 0 2 2 0 2 2 2 0 2 2 2 2 0 0 2 0 2 0 0 0 2 0 0 0 0 0 2 2 0 2 2 2 0 2 2 2 2 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 2 2 0 0 2 2 2 0 2 2 2 0 2 2 0 0 2 2 2 0 2 0 2 0 0 2 2 0 0 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0 0 2 2 2 2 0 2 0 2 2 0 0 2 0 2 2 0 2 0 2 0 0 2 0 2 0 0 0 0 2 2 0 2 0 0 2 2 2 2 0 2 2 0 2 0 0 0 2 0 2 2 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+46x^56+16x^57+66x^58+68x^59+329x^60+240x^61+388x^62+432x^63+786x^64+512x^65+964x^66+536x^67+1029x^68+512x^69+680x^70+432x^71+454x^72+240x^73+202x^74+68x^75+109x^76+16x^77+4x^78+36x^80+19x^84+4x^88+2x^92+1x^96 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 4.37 seconds.