The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X X 1 X 1 1 1 1 X 1 1 X 1 1 X^2 1 0 X 1 X^2 1 1 X^2 1 1 0 0 1 X^2 X X 1 X X 1 0 X 0 0 0 X X^2+X X 0 X^2 X^2 0 X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2 0 0 X^2+X X^2 X^2+X 0 X^2 X X X^2 X 0 X X^2+X X^2 X 0 X^2+X 0 X^2+X X^2 X^2+X X 0 X^2+X X^2+X X^2 X^2 X 0 X X X^2+X X X^2 X^2+X X X X X^2 0 X^2 X^2 0 0 X^2+X X^2+X X^2 X^2 0 0 X 0 X X X^2+X 0 0 0 X^2+X X^2+X X X X^2 0 X X^2 0 X^2+X X^2+X X^2 X^2+X X^2 0 X^2 X X^2 X X X 0 X^2 0 X X X^2 X^2 X^2+X X^2+X X^2+X X X^2 0 X X X^2 0 X^2+X X^2 X^2+X 0 0 X X^2 X 0 X X X X X^2 X X^2+X X X^2 X^2 X^2+X 0 0 0 0 X X 0 X^2+X X X^2 X^2+X X X^2 X^2 X X X^2 0 X^2+X 0 X X^2 X X 0 0 X X^2 X^2+X X^2+X X X X^2+X X^2+X X^2+X 0 0 X^2 0 X^2 X^2 X 0 X X^2+X X^2 X^2+X X X^2+X X X^2 X^2+X X^2+X X 0 X^2+X X^2 X^2+X 0 0 0 0 0 X^2 X^2+X X^2+X X^2 X X^2+X X 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+62x^60+82x^61+132x^62+188x^63+190x^64+250x^65+320x^66+360x^67+355x^68+382x^69+357x^70+316x^71+283x^72+218x^73+133x^74+112x^75+97x^76+80x^77+57x^78+32x^79+34x^80+12x^81+23x^82+16x^83+2x^84+1x^86+1x^102 The gray image is a linear code over GF(2) with n=276, k=12 and d=120. This code was found by Heurico 1.16 in 1.45 seconds.