The generator matrix 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 X 1 0 1 0 1 1 1 1 X 1 1 1 1 1 1 X 1 0 1 0 X^2 1 0 X 0 X^2+X 0 X^2+X 0 X^2+X 0 X^2+X X^2 0 X^2+X X^2+X X 0 X^2 0 X^2 0 X^2+X X X^2 X^2+X X X^2+X X X^2+X X^2+X X^2+X X X X X 0 X^2+X X^2 X^2+X X^2 X^2+X 0 0 X^2+X X^2 X^2+X X X X X 0 X^2+X 0 0 X^2 0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 0 0 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 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 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 0 0 X^2 0 X^2 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 0 0 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 0 0 X^2 X^2 0 0 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 X^2 0 0 generates a code of length 51 over Z2[X]/(X^3) who´s minimum homogenous weight is 42. Homogenous weight enumerator: w(x)=1x^0+63x^42+42x^43+113x^44+96x^45+174x^46+212x^47+304x^48+428x^49+389x^50+504x^51+402x^52+396x^53+291x^54+236x^55+145x^56+100x^57+69x^58+30x^59+41x^60+4x^61+29x^62+13x^64+7x^66+4x^68+1x^70+1x^72+1x^78 The gray image is a linear code over GF(2) with n=204, k=12 and d=84. This code was found by Heurico 1.16 in 3.53 seconds.