The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 X 1 1 a*X 1 1 1 1 1 0 1 1 a*X 1 1 1 1 a^2*X 1 1 1 a^2*X 1 1 1 1 1 1 1 a*X 1 1 X 1 1 0 1 1 1 X 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 a a^2 0 a^2*X+1 a^2*X+a^2 a 1 0 a^2*X+1 a 1 a^2*X+a^2 X a^2*X+a^2 X+a a^2*X+1 1 a^2*X+a^2 a 1 0 a*X+a a*X+a^2 a^2*X+1 a*X+1 1 a^2*X a*X+1 1 X+a 0 a*X+a^2 a*X+1 1 a*X+a a*X+1 a*X+1 1 X+a^2 a^2 X+1 a^2*X a^2*X+1 a*X a*X+a^2 1 0 X+a 1 a^2*X+a 1 1 X+a^2 X+a a*X 1 a^2*X+1 X+1 a*X+1 a*X X+a^2 a^2*X a^2*X+a^2 X+a 1 1 X a^2 X a*X+a^2 a*X+a^2 1 0 0 0 a^2*X 0 0 0 X X X X X X a^2*X a^2*X a*X X a*X a^2*X a^2*X 0 a^2*X a^2*X a*X a^2*X a*X 0 a*X X X a^2*X a*X a^2*X 0 a^2*X a*X 0 a*X a*X X a*X a^2*X a^2*X X X X a*X a*X a*X X a*X X a^2*X a*X 0 0 a^2*X a*X X 0 0 a^2*X 0 a*X 0 0 0 X a^2*X 0 0 a*X a^2*X a^2*X 0 X a*X 0 0 0 X 0 X a^2*X 0 X a^2*X X 0 a*X a^2*X 0 a^2*X 0 0 a*X a*X X X a^2*X a^2*X 0 a*X a*X 0 a^2*X X X a*X X X 0 X a^2*X X 0 X X a*X a*X X 0 0 X a^2*X a*X a^2*X a^2*X a*X a^2*X a*X a*X a^2*X a^2*X 0 a*X a^2*X X X 0 a^2*X 0 a*X a*X X a^2*X X X a*X X a^2*X a^2*X X 0 0 0 0 a^2*X a^2*X X a^2*X a*X 0 a^2*X X X a*X X a*X a*X X a^2*X a^2*X 0 a^2*X a^2*X X 0 a^2*X 0 a^2*X a^2*X a*X X X a*X X a^2*X X 0 a*X a*X 0 a*X 0 X X a*X a*X X 0 X X X a*X a^2*X X a*X a*X a*X 0 0 a*X a*X a*X 0 0 a*X 0 X 0 a*X 0 a*X a*X 0 a*X a^2*X 0 generates a code of length 76 over F4[X]/(X^2) who�s minimum homogenous weight is 212. Homogenous weight enumerator: w(x)=1x^0+99x^212+48x^213+144x^215+900x^216+336x^217+420x^219+1302x^220+408x^221+492x^223+1767x^224+660x^225+588x^227+2022x^228+528x^229+600x^231+1995x^232+456x^233+588x^235+1524x^236+456x^237+204x^239+423x^240+180x^241+36x^243+93x^244+24x^248+12x^252+30x^256+27x^260+9x^264+3x^268+3x^272+3x^276+3x^284 The gray image is a linear code over GF(4) with n=304, k=7 and d=212. This code was found by Heurico 1.16 in 1.74 seconds.