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 1 1 1 1 1 X 1 0 1 1 1 1 X 1 1 1 1 0 1 X 0 1 X 1 1 0 1 X 1 0 1 0 1 X 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X X^2 X^2+X 0 X^2+X X 0 X^2 X^2+X 0 X^2+X X X^2 X^2+X 0 X^2 X^2+X X X^2+X X X 0 X^2 0 X^2 0 X^2+X X^2+X X X^2+X X X X^2+X X 0 0 X^2+X X^2 X^2 X^2 0 X 0 X^2+X X 0 X^2+X X X^2+X X X^2 X^2+X X^2 X X^2 X^2 X^2 X^2+X X^2+X 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 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 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 58. Homogenous weight enumerator: w(x)=1x^0+83x^58+115x^60+40x^61+203x^62+80x^63+269x^64+120x^65+258x^66+160x^67+234x^68+88x^69+163x^70+16x^71+118x^72+8x^73+47x^74+26x^76+9x^78+2x^80+4x^82+1x^86+2x^88+1x^108 The gray image is a linear code over GF(2) with n=264, k=11 and d=116. This code was found by Heurico 1.16 in 4.78 seconds.