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 X 0 X 1 1 1 0 X 0 1 1 1 X 0 1 X 0 1 1 1 X 1 1 0 X 1 X 1 X 1 X 1 1 X 1 X X X 0 0 1 1 X 1 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 X^2+X 0 X X^2 X^2+X 0 X X^2+X X^2+X X X^2+X X^2+X 0 0 X X^2+X X 0 X^2+X X^2 X^2+X X X^2+X X^2+X X X 0 X^2 X^2+X X 0 X X^2+X X X^2 X 0 X^2 X^2+X X^2 X^2+X X^2+X X X^2+X X 0 X X 0 X^2 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 X^2 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 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 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 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 generates a code of length 67 over Z2[X]/(X^3) who´s minimum homogenous weight is 52. Homogenous weight enumerator: w(x)=1x^0+78x^52+30x^54+338x^56+262x^58+16x^59+802x^60+128x^61+908x^62+448x^63+1835x^64+896x^65+1816x^66+1120x^67+2167x^68+896x^69+1510x^70+448x^71+1249x^72+128x^73+502x^74+16x^75+445x^76+80x^78+179x^80+12x^82+59x^84+13x^88+1x^92+1x^96 The gray image is a linear code over GF(2) with n=268, k=14 and d=104. This code was found by Heurico 1.16 in 24 seconds.