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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 1 1 1 1 1 1 1 1 X 1 1 X 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 0 0 X^3 X^3 X^3 X^3 0 X^3 0 X^3 0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 0 0 X^3 0 X^3 0 0 X^3 X^3 X^3 0 0 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 X^3 0 0 X^3 0 0 0 X^3 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 0 0 X^3 0 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 X^3 X^3 0 X^3 X^3 0 X^3 0 0 0 X^3 0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 X^3 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 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 0 X^3 0 0 0 0 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 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 0 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 0 X^3 0 X^3 0 X^3 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 0 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0 0 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 0 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 0 X^3 X^3 X^3 X^3 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 0 0 X^3 generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 60. Homogenous weight enumerator: w(x)=1x^0+91x^60+139x^64+256x^65+1152x^66+256x^67+88x^68+8x^72+44x^76+12x^80+1x^124 The gray image is a linear code over GF(2) with n=528, k=11 and d=240. This code was found by Heurico 1.16 in 108 seconds.