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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 0 X 0 0 0 0 0 0 0 0 0 a*X a^2*X a*X X a*X a^2*X a*X X 0 a*X 0 a*X X X a^2*X a*X a*X 0 a^2*X X a*X a^2*X X a*X a*X a^2*X a*X a^2*X X a*X 0 0 a^2*X a*X 0 a^2*X a*X a*X X 0 0 a*X 0 X X a^2*X X 0 X X X X a*X a*X a*X a^2*X 0 a*X 0 a^2*X a^2*X a^2*X X 0 X X 0 0 X 0 0 0 0 X X X a*X 0 a*X a*X a*X a^2*X 0 a^2*X a^2*X X X a*X 0 X 0 a*X a*X X X a^2*X 0 a^2*X a^2*X a*X X 0 0 0 X X a*X 0 X X a*X a*X X a^2*X a^2*X a^2*X a*X 0 0 a^2*X a^2*X a^2*X a^2*X X 0 a*X X 0 a^2*X a^2*X 0 X a^2*X X 0 0 X a^2*X X a*X X a*X a^2*X 0 0 0 X 0 0 X a^2*X a*X a*X a*X 0 a^2*X a*X a*X X a^2*X a*X a*X 0 a^2*X X a^2*X X a*X X 0 X a*X 0 X X X 0 0 X a^2*X a^2*X a*X a*X X 0 0 a^2*X 0 X a^2*X 0 a^2*X a^2*X a*X X X a^2*X a^2*X X a*X a^2*X 0 0 0 0 X a^2*X X a^2*X X a*X a*X a^2*X X a*X a*X 0 a^2*X 0 X 0 0 0 0 X 0 a^2*X 0 X a*X a^2*X a^2*X X 0 0 a*X 0 a*X 0 X a*X X 0 a*X X a*X X a*X X 0 a*X a^2*X a^2*X a^2*X X a*X a*X X 0 a^2*X X a*X X a*X a^2*X a^2*X X 0 a^2*X a*X a^2*X 0 X a*X a*X 0 a*X a*X X 0 X a^2*X X a*X a*X 0 0 a*X 0 X a*X a*X X 0 a^2*X a^2*X a*X 0 0 0 0 0 X X X a^2*X X X a*X X 0 a*X a^2*X a^2*X a*X a*X a*X a*X a^2*X X a*X a*X a*X X a*X a*X a*X a^2*X a^2*X 0 0 a^2*X 0 X 0 0 0 X X 0 a^2*X a*X X a*X a*X 0 0 a*X X a^2*X 0 a*X 0 a^2*X a^2*X a^2*X 0 0 a^2*X a*X a*X X a*X a^2*X a^2*X a^2*X X a*X X X a*X a*X X a*X generates a code of length 77 over F4[X]/(X^2) who´s minimum homogenous weight is 208. Homogenous weight enumerator: w(x)=1x^0+156x^208+345x^212+411x^216+48x^219+387x^220+576x^223+468x^224+2592x^227+420x^228+5184x^231+282x^232+3888x^235+306x^236+324x^240+297x^244+210x^248+159x^252+156x^256+51x^260+57x^264+48x^268+15x^272+3x^292 The gray image is a linear code over GF(4) with n=308, k=7 and d=208. This code was found by Heurico 1.16 in 3.59 seconds.