The generator matrix 1 0 0 0 0 0 1 1 1 X 1 1 X 1 0 0 1 1 0 X 0 0 0 1 1 1 X X X 1 1 1 1 1 0 1 1 0 1 X 1 1 1 X X 0 1 0 1 1 X 1 1 0 1 0 0 0 0 0 0 0 1 1 X+1 0 X+1 1 1 X+1 1 1 X 0 X 1 0 X X 1 0 1 1 1 X+1 0 X+1 0 0 X+1 1 X X 1 X+1 X 1 1 X X+1 1 X X 1 1 0 0 0 1 0 0 0 0 0 0 0 1 X+1 1 X 0 X+1 X+1 0 X 1 1 1 1 X+1 X+1 X+1 X+1 1 X+1 0 X X+1 1 X X 1 X 0 1 1 1 X 1 0 1 0 0 X 1 X+1 1 1 0 0 0 0 1 0 0 0 1 1 1 0 X+1 X+1 1 1 X+1 1 0 X 1 X X 0 1 X X X X+1 X+1 X+1 X X X 1 1 1 X+1 1 1 X+1 1 0 0 X 0 X X+1 1 0 0 X 0 0 0 0 0 0 1 0 1 1 0 1 0 1 X+1 X X X+1 X X 1 X 1 X+1 0 X+1 X X+1 X+1 X+1 1 X 1 X+1 0 1 0 X 1 0 0 X+1 X+1 X+1 1 0 X 0 0 1 1 X X 0 0 0 0 0 0 0 1 1 0 1 1 X X+1 X+1 1 1 X 0 X+1 0 0 0 X+1 0 X 0 X+1 X+1 0 1 X 0 X 1 1 1 0 1 0 1 X X 0 0 1 0 1 0 X X 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X 0 X 0 X X X 0 X X 0 X X 0 0 0 0 0 0 0 0 X 0 0 X 0 X X X X 0 0 X X 0 X 0 0 X 0 0 X X 0 0 X 0 0 0 0 0 0 X 0 X X X X X 0 X X X 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 X X 0 X X X X X 0 X 0 X 0 X 0 0 0 0 X X 0 0 0 X X X 0 X 0 0 X X 0 X 0 X X X X 0 0 0 generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 39. Homogenous weight enumerator: w(x)=1x^0+32x^39+129x^40+220x^41+324x^42+474x^43+688x^44+808x^45+1085x^46+1302x^47+1478x^48+1858x^49+2008x^50+2186x^51+2404x^52+2402x^53+2407x^54+2420x^55+2132x^56+1942x^57+1729x^58+1318x^59+1049x^60+776x^61+503x^62+402x^63+245x^64+170x^65+118x^66+50x^67+58x^68+14x^69+13x^70+4x^71+7x^72+2x^73+5x^74+4x^75+1x^76 The gray image is a linear code over GF(2) with n=106, k=15 and d=39. This code was found by Heurico 1.16 in 98.4 seconds.