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 X 0 1 1 1 X 0 1 1 1 1 1 X 1 0 1 1 1 0 1 1 1 X 1 X 0 1 1 0 0 1 1 X^2 1 0 X 0 X^2+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 0 0 X^2 X^2+X X^2+X X^2+X X 0 X^2 X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X X X^2+X 0 X^2 X 0 X 0 X^2+X X X^2+X X X^2 X^2 X X X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 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 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 0 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 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 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 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 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 0 0 X^2 generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 48. Homogenous weight enumerator: w(x)=1x^0+112x^48+4x^49+104x^50+48x^51+324x^52+208x^53+236x^54+464x^55+313x^56+600x^57+204x^58+464x^59+290x^60+208x^61+196x^62+48x^63+163x^64+4x^65+28x^66+52x^68+18x^72+6x^76+1x^88 The gray image is a linear code over GF(2) with n=228, k=12 and d=96. This code was found by Heurico 1.16 in 1.28 seconds.