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 0 1 1 1 1 (a+1)X (a+1)X 0 1 1 1 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 aX a+1 aX+a X+1 (a+1)X+a+1 1 1 1 X (a+1)X+a+1 aX+a 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 1 X (a+1)X+a (a+1)X 0 0 (a+1)X+1 a+1 (a+1)X 1 a+1 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 aX 0 0 (a+1)X (a+1)X 0 0 0 X (a+1)X aX 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+780x^270+756x^271+159x^272+1728x^274+1200x^275+213x^276+1908x^278+1164x^279+174x^280+1404x^282+948x^283+168x^284+1212x^286+960x^287+135x^288+924x^290+420x^291+84x^292+684x^294+408x^295+45x^296+324x^298+168x^299+36x^300+216x^302+120x^303+3x^304+36x^306+3x^308+3x^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 8.67 seconds.