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 X X 1 1 1 1 X X 1 1 1 X 1 1 1 1 1 1 X 1 X 1 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 X X X a^2*X a^2*X 0 0 X a*X X X 0 0 a^2*X a^2*X a^2*X 0 a*X 0 0 a^2*X X a^2*X 0 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^2*X a*X 0 a^2*X 0 0 X a^2*X a^2*X a*X 0 X X 0 a*X X a^2*X X X X a^2*X a*X X 0 0 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 0 a^2*X a*X 0 a^2*X X a^2*X 0 a^2*X 0 0 X X a*X X X a^2*X a^2*X a^2*X a^2*X a*X X X X 0 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^2*X a*X a*X X a^2*X 0 0 a*X X 0 a*X a*X a^2*X a^2*X X 0 a*X 0 X a*X a^2*X 0 a^2*X a*X 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 a*X 0 a^2*X 0 a^2*X 0 a*X 0 a^2*X X a^2*X 0 a^2*X 0 a^2*X a*X 0 a*X a^2*X X a^2*X a^2*X a^2*X a^2*X a^2*X a*X generates a code of length 76 over F4[X]/(X^2) who´s minimum homogenous weight is 204. Homogenous weight enumerator: w(x)=1x^0+96x^204+303x^208+396x^212+168x^215+426x^216+648x^219+447x^220+2256x^223+378x^224+3792x^227+342x^228+3720x^231+333x^232+1704x^235+288x^236+282x^240+249x^244+225x^248+123x^252+84x^256+54x^260+48x^264+18x^268+3x^276 The gray image is a linear code over GF(4) with n=304, k=7 and d=204. This code was found by Heurico 1.16 in 3.53 seconds.