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 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 0 X^3 0 0 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 0 0 X^3 X^3 0 0 0 X^3 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 0 0 0 0 0 0 0 0 X^3 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 X^3 0 0 0 0 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 0 0 0 X^3 0 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 0 0 0 0 0 X^3 0 0 0 X^3 X^3 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 0 0 0 0 0 X^3 0 X^3 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 0 X^3 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 X^3 0 X^3 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 0 0 0 0 0 X^3 X^3 0 X^3 X^3 0 0 0 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 generates a code of length 68 over Z2[X]/(X^4) who´s minimum homogenous weight is 62. Homogenous weight enumerator: w(x)=1x^0+56x^62+94x^64+64x^66+256x^67+1152x^68+256x^69+112x^70+24x^78+32x^80+1x^128 The gray image is a linear code over GF(2) with n=544, k=11 and d=248. This code was found by Heurico 1.16 in 33.9 seconds.