The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 (a+1)X 1 0 1 1 1 X 1 1 1 1 1 1 1 aX 1 1 1 aX 1 1 0 (a+1)X 1 aX 1 aX 1 1 1 aX 1 1 1 1 1 aX (a+1)X 1 (a+1)X 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 (a+1)X 1 1 1 0 1 1 0 1 aX 1 aX 1 1 X X 1 1 1 0 1 1 1 1 0 0 1 0 0 X aX 1 (a+1)X+a a+1 (a+1)X+1 X+1 X+a aX+1 X+a+1 1 a+1 1 X+a (a+1)X+a aX+a+1 1 (a+1)X aX X+a X 1 X+1 aX+a+1 1 1 0 aX+a 0 a 1 1 1 a 1 X+a+1 (a+1)X aX+a+1 X+a+1 X+1 1 (a+1)X+a X+a+1 (a+1)X a+1 X+a+1 1 1 aX+a 1 (a+1)X+a X+1 aX+a X (a+1)X a aX X+1 (a+1)X+a (a+1)X+a+1 (a+1)X a a+1 aX a+1 1 aX+a+1 (a+1)X aX 1 aX+a+1 (a+1)X+1 1 (a+1)X 1 1 (a+1)X 0 X+a 1 0 (a+1)X+a a+1 aX+a 1 X+1 (a+1)X+a+1 aX a+1 1 0 0 1 1 (a+1)X+a (a+1)X+a+1 a+1 aX+a+1 X+a+1 X+a X+1 a (a+1)X aX+a 1 X+1 a (a+1)X (a+1)X+1 aX (a+1)X+a+1 X+a+1 0 a 1 (a+1)X+1 aX X+a (a+1)X+a X+a 0 (a+1)X+a 1 (a+1)X+a+1 X+a+1 (a+1)X+a X+a+1 (a+1)X+a 0 a 1 1 X aX 0 (a+1)X aX+a+1 (a+1)X+a aX+a+1 0 a 1 X+a+1 X+a+1 aX+1 a+1 (a+1)X+a+1 X+1 aX+a+1 X a a (a+1)X+1 X+a 1 X (a+1)X+1 aX+a+1 aX+1 X X+a X+1 (a+1)X+1 a aX+a+1 aX (a+1)X+a+1 aX+a (a+1)X+1 a 1 X X+a (a+1)X+1 1 a+1 (a+1)X+1 aX+a+1 X (a+1)X+a+1 0 aX (a+1)X (a+1)X 0 0 0 (a+1)X 0 0 0 0 0 0 0 0 0 0 X aX X (a+1)X aX (a+1)X (a+1)X X X aX aX X X aX aX (a+1)X aX (a+1)X aX (a+1)X (a+1)X (a+1)X aX X X (a+1)X (a+1)X 0 aX (a+1)X (a+1)X 0 (a+1)X (a+1)X aX X 0 (a+1)X aX 0 (a+1)X X X X aX X X aX X aX X aX (a+1)X (a+1)X X aX (a+1)X 0 (a+1)X aX X aX aX aX aX X X 0 X 0 (a+1)X aX X 0 X X (a+1)X aX X 0 generates a code of length 94 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 270. Homogenous weight enumerator: w(x)=1x^0+840x^270+696x^271+147x^272+1620x^274+1152x^275+261x^276+1884x^278+1272x^279+177x^280+1596x^282+1128x^283+156x^284+1116x^286+672x^287+60x^288+876x^290+612x^291+96x^292+672x^294+324x^295+81x^296+336x^298+204x^299+36x^300+240x^302+60x^303+3x^304+36x^306+24x^307+3x^308+3x^320 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 13.4 seconds.