The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 X 1 aX 1 1 1 1 (a+1)X 1 1 1 1 1 1 1 1 1 1 1 1 aX X aX 1 1 1 1 1 1 1 1 1 1 0 1 1 X aX (a+1)X X 1 1 1 0 1 0 (a+1)X X aX 1 (a+1)X+a a+1 (a+1)X+1 X+1 aX+1 X+a+1 1 a 1 (a+1)X+a X+a (a+1)X+a+1 aX+a+1 1 0 aX+a (a+1)X+1 X+a X+a+1 (a+1)X+a+1 aX+a+1 aX+a (a+1)X X+1 a+1 (a+1)X+1 0 1 1 X aX+a X+a+1 X+1 (a+1)X+a 1 (a+1)X+a+1 a X+1 aX+1 1 (a+1)X+a+1 X+a+1 1 1 1 1 aX+a aX+1 aX+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+1)X aX+a X+a+1 a (a+1)X+1 aX aX+1 0 X+1 a X 1 aX+a X (a+1)X+1 X+a+1 (a+1)X X+a (a+1)X+1 X a a+1 1 (a+1)X (a+1)X+a X+a aX+a+1 aX a 1 (a+1)X+1 a X (a+1)X+1 (a+1)X+a+1 X a+1 (a+1)X 1 X+a a+1 X+1 (a+1)X+a+1 X+a X+1 generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 161. Homogenous weight enumerator: w(x)=1x^0+444x^161+504x^162+240x^163+9x^164+468x^165+528x^166+144x^167+27x^168+324x^169+324x^170+72x^171+21x^172+132x^173+180x^174+60x^175+288x^177+84x^178+48x^179+72x^181+108x^182+12x^183+6x^188 The gray image is a linear code over GF(4) with n=224, k=6 and d=161. This code was found by Heurico 1.16 in 24.3 seconds.