The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a^2*X X 1 1 a*X 1 1 1 1 1 1 1 a*X 1 1 1 1 1 1 0 1 1 1 1 1 X 1 1 1 1 1 0 1 1 1 a^2*X 0 1 1 1 1 0 a*X a^2*X 1 a^2*X X 1 a^2*X 1 1 1 1 1 1 1 0 1 1 1 1 1 a*X X 1 1 1 1 1 1 0 1 1 0 X 1 a^2*X 1 1 1 0 1 0 0 X a^2*X 1 a^2*X+a a^2 a^2*X+1 a*X+1 a*X+a X+1 X+a 1 1 a^2*X+a^2 a*X+a^2 1 a^2*X+a a^2 a^2*X a*X+a a*X+a^2 0 a^2*X 1 a^2*X+1 a*X+a a^2*X+a a^2*X+a^2 a*X+a X+a^2 X a*X+1 X+1 a^2*X+a^2 X+a a*X+a^2 1 a^2*X+1 1 X X+1 X+1 1 a a^2*X 1 1 X a*X a^2*X+1 a^2*X a*X+a^2 1 1 1 a^2*X+a^2 a*X 1 X+1 1 X+a a^2 a^2*X+a^2 a^2*X+a 0 a*X+a a*X 1 a a a^2*X+a 1 1 1 1 a^2*X+a 1 a*X+a^2 X 0 X+a^2 1 a^2*X X+1 1 1 X+1 1 a^2*X+a^2 X+1 a^2 0 0 1 1 a^2*X+a a^2 X+a^2 a^2*X+a^2 a*X+a^2 X+a 1 a*X+a X a^2*X a^2*X+a^2 a*X+a a*X a X+1 X+1 a^2*X+1 1 a^2*X+1 a*X+1 X a a^2*X+1 a*X X+a^2 X+a a^2*X+a^2 0 a*X 1 X+a X+1 X a^2*X+a a*X+a a X+1 a^2 a^2 a*X a*X+1 a^2*X a^2*X+1 a^2*X a X+a 1 a^2*X X+a^2 X+a^2 a*X+a a^2*X+1 a^2 a^2*X a^2*X+1 1 a*X+a a^2 X X a^2*X+a a 1 a^2*X+a X+a a^2*X+a^2 1 X+a a*X+a^2 X+a^2 X+a^2 a X+a a*X+a^2 a^2*X+1 1 0 X+1 a^2*X+a^2 a*X+a^2 0 0 a*X 1 a^2*X 1 X a^2*X a^2 X 0 0 0 a^2*X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a^2*X a^2*X a*X a*X a*X a*X a^2*X a^2*X a*X X X a*X a^2*X a^2*X X a*X a*X X a*X a^2*X a*X X a*X a^2*X X a^2*X a*X X X a^2*X a^2*X a*X a^2*X a^2*X a*X X X a^2*X X X a^2*X X X a^2*X a^2*X a^2*X a*X a^2*X a*X 0 a*X X a^2*X a*X a^2*X a*X X a*X a*X a*X X a*X X X a^2*X a*X X a^2*X a*X 0 a^2*X X X 0 0 generates a code of length 94 over F4[X]/(X^2) who´s minimum homogenous weight is 270. Homogenous weight enumerator: w(x)=1x^0+744x^270+804x^271+153x^272+1716x^274+1164x^275+189x^276+2016x^278+1164x^279+240x^280+1308x^282+972x^283+159x^284+1308x^286+804x^287+108x^288+840x^290+540x^291+39x^292+696x^294+420x^295+108x^296+348x^298+180x^299+21x^300+228x^302+72x^303+12x^306+24x^307+6x^312 The gray image is a linear code over GF(4) with n=376, k=7 and d=270. This code was found by Heurico 1.16 in 1.89 seconds.