The generator matrix 1 0 1 1 1 X+2 1 1 0 1 1 X+2 0 1 1 X+2 1 1 X 1 1 0 1 1 1 0 1 1 1 X+2 1 1 X+2 1 1 X+2 1 1 1 X+2 1 0 0 0 1 2 1 1 0 1 1 1 1 2 X+2 1 1 1 1 1 1 1 2 1 1 2 X+2 0 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+3 0 1 X+2 3 3 1 0 X+2 X+1 1 X+1 3 1 0 X+2 1 X+1 2 0 1 X+1 1 1 1 X+2 1 3 0 1 3 0 X+1 X 1 1 3 0 X+1 X+3 X+1 2 X+2 1 1 2 1 1 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 2 2 2 0 2 0 0 2 0 0 0 2 2 0 0 0 2 2 0 2 2 2 0 2 0 0 0 2 2 2 2 2 2 2 0 2 0 0 2 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 0 2 2 0 0 2 2 2 2 0 0 0 2 2 0 2 0 2 0 2 2 0 2 0 0 2 0 2 0 2 2 0 2 2 0 0 2 0 2 0 0 2 0 2 0 2 0 0 0 0 2 0 0 0 0 0 0 2 2 0 2 2 2 0 0 0 2 2 2 0 2 2 0 2 0 2 2 2 0 2 0 2 0 0 0 2 2 0 2 0 0 0 0 0 0 2 0 2 2 2 0 0 0 2 0 0 2 2 0 2 0 0 2 0 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 0 0 2 0 2 2 0 2 0 2 0 2 2 2 0 0 2 0 0 2 2 2 0 0 0 0 2 0 0 0 2 2 2 0 2 0 2 0 2 0 2 0 0 2 0 2 0 2 2 2 0 2 0 0 0 0 0 0 0 2 0 0 2 2 0 0 2 2 0 0 2 0 2 0 2 2 2 0 2 2 2 0 0 0 0 2 0 0 0 2 0 0 2 2 2 0 0 2 0 0 2 2 0 0 0 2 0 2 0 2 2 2 2 2 2 2 2 2 2 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 2 2 0 0 0 0 2 2 2 2 2 0 2 2 0 2 2 2 2 2 2 0 2 2 2 0 2 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 0 0 2 2 2 0 0 0 2 2 2 2 0 0 2 0 2 0 0 0 2 2 0 2 2 2 2 0 2 0 0 0 2 0 2 2 2 2 2 0 2 0 0 2 0 0 2 0 0 0 0 2 0 2 2 2 generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+56x^58+221x^60+56x^61+427x^62+200x^63+769x^64+344x^65+1072x^66+424x^67+1129x^68+424x^69+1064x^70+344x^71+735x^72+200x^73+385x^74+56x^75+181x^76+44x^78+20x^80+14x^82+11x^84+8x^86+3x^88+1x^90+2x^92+1x^94 The gray image is a code over GF(2) with n=272, k=13 and d=116. This code was found by Heurico 1.16 in 4.54 seconds.