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 X 1 1 1 1 1 1 X 1 1 1 X X 1 1 X 1 X X 1 1 1 1 0 X 0 0 0 0 0 0 0 0 0 a*X a^2*X X a^2*X X a^2*X a*X a^2*X a^2*X a*X 0 a^2*X a*X X X a^2*X a*X a*X X 0 a*X a*X a*X 0 X a*X a^2*X 0 a^2*X a^2*X a*X a*X a*X a*X a*X a^2*X a*X a*X 0 0 0 0 a*X X a*X X 0 0 a*X a^2*X a*X a^2*X 0 a^2*X X a*X X X 0 0 X a^2*X 0 X X X a*X 0 0 0 X 0 0 0 0 X X X a*X 0 a*X a^2*X a^2*X a^2*X a*X a^2*X a^2*X X a*X 0 X 0 a*X X X X a*X 0 a*X a*X a*X a^2*X X a*X X a*X a^2*X a*X X X a^2*X a^2*X a*X a*X 0 a*X a*X a*X a*X a*X X 0 a^2*X X X 0 X a*X 0 0 a*X X X 0 X a*X a*X a^2*X 0 a^2*X a*X 0 a^2*X a*X X a*X 0 0 0 0 X 0 0 X a^2*X a*X a*X a*X a*X 0 a^2*X a*X a*X a^2*X a*X a^2*X 0 a^2*X 0 a*X a^2*X 0 X a*X a*X 0 a*X 0 a^2*X a^2*X a*X X a*X a^2*X 0 a*X a^2*X 0 X a^2*X a*X X a^2*X a^2*X a*X X a*X X a^2*X X 0 0 X X a*X 0 X a*X a*X X X a*X 0 a^2*X a^2*X a^2*X 0 a^2*X 0 0 X X 0 a^2*X a*X 0 0 0 0 0 X 0 a^2*X 0 X a*X a^2*X a*X a^2*X 0 a*X a*X X 0 X a*X a*X X a*X a^2*X a*X 0 0 0 0 a^2*X a*X a^2*X 0 a^2*X 0 X X a^2*X a^2*X a*X 0 X a^2*X a^2*X 0 a*X a*X a*X a^2*X X a^2*X a*X a*X 0 a*X 0 a^2*X X a*X 0 X a^2*X a^2*X a*X a^2*X a^2*X a*X a^2*X a^2*X a*X 0 X 0 X a*X a*X 0 0 X 0 0 0 0 0 X X X a^2*X X X 0 a^2*X X a*X a^2*X X X a^2*X 0 a^2*X X a*X a^2*X X 0 a^2*X X X a^2*X a^2*X a*X a*X 0 0 X a*X a*X a*X 0 0 0 a^2*X X X X X 0 0 a^2*X 0 0 X a*X a^2*X a^2*X a*X X 0 a^2*X a^2*X a*X a^2*X a^2*X a*X X 0 0 a*X a^2*X a^2*X 0 0 0 a*X 0 0 a*X a^2*X generates a code of length 79 over F4[X]/(X^2) who´s minimum homogenous weight is 212. Homogenous weight enumerator: w(x)=1x^0+66x^212+291x^216+399x^220+549x^224+1191x^228+2316x^232+4305x^236+4218x^240+1887x^244+270x^248+240x^252+198x^256+195x^260+141x^264+57x^268+39x^272+9x^276+6x^280+3x^284+3x^288 The gray image is a linear code over GF(4) with n=316, k=7 and d=212. This code was found by Heurico 1.16 in 3.68 seconds.