The generator matrix 1 0 0 0 0 1 1 1 1 1 X^2 1 X^2 X^2+X X^2 1 X^2+X 1 X^2 1 1 X^2 1 1 1 X^2+X 1 X^2 1 1 X X^2+X X^2 1 1 X 0 1 1 X^2+X 0 1 X^2+X X 1 1 0 1 0 1 1 1 X^2+X 1 1 1 X X^2+X 1 1 1 X^2+X 1 1 1 X^2+X X^2 1 0 0 1 0 0 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 0 1 X^2+1 1 X^2+X+1 1 1 1 X+1 X+1 1 X+1 1 X^2+X+1 X^2+X 1 X X^2+X X^2+X+1 0 1 X^2+X X+1 X 1 X^2 X^2+1 1 X X^2+X+1 X^2+X X^2 X^2+1 1 0 X^2 X^2+X X^2+X 1 X X^2+1 X^2 1 0 1 X^2+X 1 X^2+1 1 X^2+X X^2+X X^2+X 1 X 0 0 1 0 0 0 X^2+1 X+1 1 X X X^2+X+1 1 1 1 X^2+X 1 X^2+1 X^2+X+1 1 X^2+X+1 X^2 0 0 X^2 X+1 X+1 0 0 X X+1 1 X^2+X X X+1 X^2+X X^2 X^2+X+1 0 X 0 X X 1 X+1 1 1 1 X^2+1 1 X^2+1 0 1 X^2+X X 1 X^2 X X^2 X^2+X+1 X^2 1 0 X^2+1 X^2 1 1 X X^2+X 0 0 0 1 0 1 1 X X X^2+X 1 X^2+1 X^2 1 1 X^2+X+1 1 0 0 X^2+X+1 X^2+1 X+1 X^2 1 X^2+X+1 X+1 X X X^2+X X+1 X X^2+X X X^2 1 X^2+X+1 1 X^2+X X^2 1 1 X^2+X+1 X^2+X X X^2+X+1 X^2+X X+1 X^2+X+1 X^2+X X+1 1 X^2+1 X^2+1 0 X^2 X^2+1 X^2+X 0 X^2+X+1 X^2+X+1 X^2 X^2+X 1 X X^2+X X^2 X^2+1 X+1 1 0 0 0 0 1 1 X^2 0 X+1 1 X^2+X+1 X^2+X+1 1 X^2+X X+1 0 X^2+X+1 X X^2+1 X X+1 X 1 X^2+X X+1 X^2+X X^2+1 X^2+1 0 1 X^2 X 1 0 1 1 0 0 X^2+1 X 1 X X^2+X X^2+X+1 X^2+X+1 X^2+1 X^2 X 0 X X^2+X+1 0 1 X^2+1 X+1 X+1 1 X+1 X^2+X X^2+1 X^2 X^2+X X+1 X+1 X+1 X+1 X X^2+1 1 0 0 0 0 0 X 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2+X X X X^2+X X^2+X X^2+X X X X^2+X X^2+X X X X^2+X X X X^2+X X^2 X X X^2+X X X X^2+X X X X^2 X^2+X 0 X^2+X X^2 X X 0 X generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+280x^58+684x^59+1594x^60+2128x^61+3478x^62+4764x^63+6123x^64+7832x^65+9468x^66+10868x^67+11481x^68+12452x^69+11976x^70+11480x^71+9976x^72+8260x^73+6362x^74+4560x^75+3054x^76+1692x^77+1200x^78+632x^79+374x^80+148x^81+122x^82+32x^83+31x^84+10x^86+4x^87+6x^88 The gray image is a linear code over GF(2) with n=276, k=17 and d=116. This code was found by Heurico 1.13 in 220 seconds.