The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 1 X+2 1 1 0 1 0 1 1 1 X+2 1 1 0 1 1 X+2 1 1 1 1 X+2 1 1 1 X 0 1 1 0 1 1 1 1 1 X+2 1 2 0 1 X 1 1 1 1 1 1 2 X+2 X 1 1 X+2 0 X 0 1 X+1 X+2 1 1 0 X+1 1 X+2 3 1 0 X+1 1 X+2 3 1 3 1 0 X+2 X+1 1 X+2 X+1 1 0 2 1 X+2 3 X+2 X+3 1 X 0 1 1 1 0 3 1 3 X+1 0 X X+3 1 2 1 1 X+1 1 0 2 X+2 X+3 1 3 1 1 1 0 1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 2 0 2 0 2 2 0 2 2 2 0 0 0 2 2 2 0 2 0 0 0 0 0 0 2 0 0 0 2 2 0 0 2 0 2 2 2 2 2 2 0 2 2 2 2 2 2 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 0 2 0 2 0 2 0 2 2 0 0 2 0 0 2 0 0 2 2 0 0 2 0 2 0 2 0 2 0 2 0 2 0 2 2 2 0 0 2 2 2 0 0 2 2 0 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 2 2 0 2 2 0 0 2 2 2 2 0 2 2 0 0 2 0 0 2 0 0 2 0 2 0 0 0 2 0 0 0 0 2 0 2 2 0 0 2 2 2 2 0 0 2 0 2 0 0 0 2 0 2 2 2 2 0 0 0 0 0 0 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 0 2 2 0 2 2 0 0 0 2 2 2 0 0 0 2 2 0 0 0 2 2 0 2 0 2 2 0 0 2 0 2 0 2 2 0 2 0 0 0 0 2 0 0 0 2 0 2 0 0 0 0 0 0 2 0 2 0 0 0 2 0 2 0 2 2 2 2 2 0 0 0 2 2 2 0 2 2 2 2 0 2 2 0 0 0 2 2 2 2 0 0 0 0 0 0 0 2 2 2 0 2 0 0 0 0 2 0 2 0 0 0 2 2 0 0 0 0 0 0 0 0 0 2 2 0 2 0 0 2 2 2 2 0 2 0 0 2 0 2 2 0 2 0 0 0 0 2 2 2 0 0 0 2 0 0 2 2 0 0 2 0 0 2 0 2 0 2 2 0 0 0 0 0 2 2 0 2 2 2 0 0 2 2 generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+126x^60+44x^61+178x^62+140x^63+386x^64+268x^65+398x^66+332x^67+424x^68+292x^69+370x^70+260x^71+377x^72+164x^73+202x^74+36x^75+58x^76+4x^78+23x^80+6x^84+5x^88+2x^92 The gray image is a code over GF(2) with n=272, k=12 and d=120. This code was found by Heurico 1.16 in 1.1 seconds.