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 X 1 1 1 X 1 1 1 1 1 X 1 X X 1 1 1 X 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 X a*X a*X a*X a^2*X 0 a*X a*X a^2*X a^2*X a*X 0 X X 0 a*X X a*X X 0 a*X a*X a^2*X a^2*X X a*X X X X X a^2*X 0 X 0 X 0 0 X X X a*X a*X X 0 X 0 X X a^2*X X a^2*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^2*X X 0 X a*X a^2*X a*X 0 a^2*X X 0 a*X 0 X X a*X a*X a*X a*X a^2*X X a*X X X 0 a*X X 0 a*X a^2*X a^2*X a*X X X X 0 a*X X X a^2*X a*X a^2*X a*X a^2*X a*X a^2*X 0 X a*X X a^2*X 0 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 0 X X X X X X 0 0 X a^2*X 0 X a*X a*X a*X a*X a^2*X a^2*X a*X 0 0 0 0 0 a*X 0 0 a^2*X X 0 X a*X 0 a^2*X X X X a*X a^2*X 0 X X 0 a^2*X a^2*X X a*X 0 a^2*X X X 0 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 0 a*X a*X a^2*X a^2*X a^2*X a*X a*X a*X a*X a^2*X X a*X X a*X 0 X a^2*X a*X a*X a*X a^2*X X a^2*X a^2*X a^2*X X a*X a^2*X a^2*X 0 0 a^2*X X 0 a^2*X a^2*X 0 a*X a*X 0 0 a*X 0 a^2*X 0 a*X X X a^2*X a^2*X 0 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 a*X a^2*X a^2*X a*X a^2*X a*X X a*X 0 a^2*X 0 0 a*X X X 0 a^2*X a^2*X X 0 a^2*X a^2*X X 0 a*X a*X X a^2*X a*X X X X a^2*X 0 a^2*X a*X X 0 X 0 a*X 0 a*X 0 a^2*X a^2*X X 0 a^2*X a*X a*X a*X generates a code of length 78 over F4[X]/(X^2) who´s minimum homogenous weight is 212. Homogenous weight enumerator: w(x)=1x^0+237x^212+357x^216+12x^217+411x^220+108x^221+462x^224+864x^225+408x^228+1944x^229+378x^232+3852x^233+345x^236+3900x^237+297x^240+1608x^241+270x^244+201x^248+270x^252+180x^256+102x^260+90x^264+51x^268+9x^272+15x^276+6x^280+3x^284+3x^288 The gray image is a linear code over GF(4) with n=312, k=7 and d=212. This code was found by Heurico 1.16 in 16.8 seconds.