The generator matrix 1 0 1 1 1 3X+2 1 1 0 1 3X+2 1 1 1 1 2X 1 3X 1 1 0 1 1 3X 1 1 1 1 2X+2 X 1 1 2 1 1 3X+2 2 1 1 3X 2 1 1 1 1 1 1 1 1 X 1 2 X+2 1 1 X 1 0 1 1 1 0 X 2X+2 X 1 2X 2 1 0 1 X+1 3X+2 3 1 2X+3 0 1 3X+2 1 X+1 2X+1 X+3 2X 1 3X 1 3X+3 0 1 1 3X 1 3X+3 2X+3 X+1 2 1 1 X 3X+3 1 2X+1 2X+3 1 1 1 X+2 1 1 X+1 3X 3X+1 2X+2 2X+2 3X+2 3X+3 2X+2 2X X+1 1 1 3X+2 2X+3 1 3 1 X+2 1 X+3 1 X 1 2X 1 1 1 2X 0 0 2 0 0 0 0 2 2X+2 2X+2 2 2X+2 2X 2 2X+2 2 2X 2X 2 2X 2X 2X 2 2X+2 2X+2 2 0 0 2 2X+2 2X+2 0 2X 2X+2 2 2X+2 0 2 0 2X 2X+2 2X 2X 0 2 0 2 2X+2 2X+2 2 2X 2X+2 0 2X 2 0 2X 0 2X 2 2X 2X 0 0 2X 2X+2 2X 2X+2 0 0 0 0 2X+2 2X 2X+2 2 2 2X+2 2X 0 2X+2 0 2X 0 2X 2X 2X 2X+2 2X+2 2X+2 2 2 2X+2 2 0 2X 2X+2 2 0 0 2 2 2X+2 2X+2 2 0 2X 0 2 2X 0 2X+2 2 2X 2X 2 2X 2 2X 2X 0 2X 2 2X 2X+2 2X+2 2X 0 2 2 0 0 2X+2 2 0 2X 2 2 generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+89x^64+300x^65+470x^66+530x^67+502x^68+424x^69+480x^70+516x^71+392x^72+206x^73+100x^74+52x^75+7x^76+8x^77+4x^78+4x^79+4x^81+2x^83+1x^84+1x^86+2x^89+1x^94 The gray image is a code over GF(2) with n=552, k=12 and d=256. This code was found by Heurico 1.16 in 0.437 seconds.