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 X 1 0 1 1 1 X 1 0 1 1 X 1 0 1 0 1 0 X 1 X^2 1 0 1 X 1 1 1 1 X^2 0 1 1 X X 1 1 X 1 1 1 X^2 X^2 0 X X X^2 1 0 X 0 0 0 0 0 0 X^2 X X^2+X X^2+X X X X^2+X X^2+X X^2 X^2 0 X X X^2+X X 0 X X 0 X^2+X X X^2 X^2 X^2 X^2+X X^2+X 0 X^2+X X^2+X X X^2 X^2+X X^2+X X^2+X X^2+X X X X X^2+X X X 0 X X X^2 0 X 0 X 0 X X^2+X X X^2+X X^2 X^2 X X X^2+X X X^2+X X^2 0 0 X^2 X^2 X^2+X 0 X X X X 0 X 0 0 0 X 0 0 0 X X^2+X X^2+X X X X^2 X X X^2 0 X^2 X^2+X X^2+X X^2+X 0 X X^2+X X^2+X 0 X^2+X X^2+X X^2 X^2 0 0 X^2 X^2 X^2+X 0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X 0 X 0 X^2+X X^2+X 0 0 X^2 0 X^2 X^2 X X^2+X X^2+X X^2 0 X^2 0 X^2 X X 0 X X X X X X^2 X^2+X X^2+X X X^2 X^2 0 X^2+X X^2 X X^2 X^2 X^2+X X^2 0 0 0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X X X^2 X^2 0 0 0 X^2 X^2 X^2+X X X^2+X X X 0 X X^2 X^2+X X^2+X X^2+X X X^2+X X^2+X X^2+X X X 0 X^2 X^2 X^2 0 X^2+X X^2+X X X 0 X^2+X X^2+X 0 X^2+X 0 X X^2 X X 0 X^2 X^2+X X^2 X X X X X 0 X^2+X X^2+X 0 X^2 X^2+X X X^2 X^2+X X 0 X^2+X X^2+X 0 0 X 0 0 0 0 X X X^2 X^2+X X X^2 X 0 X 0 X X X^2+X X^2+X 0 X^2 X X X^2 0 X^2 X^2+X X^2+X 0 X 0 X^2 X X^2+X X X^2+X X^2 X^2+X X^2 0 0 X X^2 0 X^2 X^2 X^2+X X^2+X 0 X^2 X^2 X X X 0 X^2 X X^2+X X^2 0 X^2+X X^2+X 0 0 0 X^2+X 0 0 X^2 X 0 X X^2+X X^2 X^2 0 0 X^2+X X X^2+X 0 0 X^2 X 0 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 0 0 X^2 0 generates a code of length 83 over Z2[X]/(X^3) who´s minimum homogenous weight is 74. Homogenous weight enumerator: w(x)=1x^0+114x^74+12x^75+296x^76+88x^77+352x^78+140x^79+397x^80+176x^81+412x^82+188x^83+535x^84+184x^85+352x^86+148x^87+231x^88+64x^89+134x^90+24x^91+92x^92+76x^94+34x^96+28x^98+13x^100+4x^102+1x^120 The gray image is a linear code over GF(2) with n=332, k=12 and d=148. This code was found by Heurico 1.16 in 2.06 seconds.