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 X 1 1 1 0 1 1 1 X 1 1 1 0 1 X 1 1 1 0 1 1 1 1 X 1 0 1 1 1 1 0 1 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^2 X X^2+X X 0 0 X^2 X^2 0 X^2 X^2+X X^2+X X X^2+X X X 0 X^2+X X^2+X X^2+X X^2+X 0 X 0 X^2+X 0 X^2 0 X X^2 0 X 0 X^2+X X^2+X X X 0 0 X^2 X X^2 X^2 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 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 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 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 X^2 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 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0 0 0 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 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 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 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 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 X^2 0 generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 53. Homogenous weight enumerator: w(x)=1x^0+50x^53+48x^54+72x^55+101x^56+88x^57+128x^58+184x^59+224x^60+236x^61+278x^62+184x^63+164x^64+88x^65+32x^66+72x^67+50x^69+20x^70+18x^72+6x^78+3x^80+1x^104 The gray image is a linear code over GF(2) with n=244, k=11 and d=106. This code was found by Heurico 1.16 in 8.29 seconds.