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 X X 1 1 1 1 1 0 X X 0 1 1 1 1 0 X X 1 1 1 X^2 1 X^2 X^2 X^2 1 1 1 X 0 X 0 X 0 0 X X^2+X 0 X^2 X^2+X X 0 X X 0 X^2 X^2 X^2+X X 0 0 X X^2 X^2 X 0 X^2+X X^2+X X^2 X^2 0 X X^2+X X 0 X^2 X^2 0 X^2 X^2 X^2+X X^2+X X 0 X X^2+X X^2 X X 0 X X^2+X X X X X^2+X X^2+X X^2 X^2+X 0 0 X X 0 X^2+X X 0 X^2 X 0 X 0 X^2+X X^2 X^2+X X X X^2 0 X^2 0 X^2+X X^2 X^2 X^2+X X X X^2+X X X X^2+X X 0 0 X^2 X^2 X X^2+X X^2+X X X 0 X^2+X X X^2 X^2 X X^2 X^2 X X X X X^2+X X X X^2+X X^2+X 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 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 0 0 X^2 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 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 X^2 0 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+204x^52+12x^53+184x^54+80x^55+412x^56+184x^57+444x^58+240x^59+648x^60+240x^61+462x^62+176x^63+342x^64+72x^65+150x^66+16x^67+144x^68+4x^69+34x^70+32x^72+6x^74+3x^76+5x^80+1x^92 The gray image is a linear code over GF(2) with n=240, k=12 and d=104. This code was found by Heurico 1.16 in 66.7 seconds.