The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 X 1 1 1 1 1 1 1 X 1 1 1 1 aX 1 1 1 1 1 1 1 X 1 X 0 1 1 1 1 1 1 1 1 1 1 0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a (a+1)X+a+1 1 0 a (a+1)X+1 1 (a+1)X+a+1 X+a 1 X (a+1)X+1 aX+a+1 X+a X 1 aX+a+1 1 X aX+1 a+1 X+a 1 0 X aX aX+1 aX+1 a (a+1)X+a 1 aX+a+1 1 1 aX+a X+a+1 X+1 a+1 X+a+1 1 aX a+1 aX+1 0 0 0 (a+1)X 0 X X (a+1)X X (a+1)X X 0 0 X X 0 (a+1)X aX aX 0 (a+1)X aX (a+1)X aX aX (a+1)X X X 0 X (a+1)X (a+1)X (a+1)X 0 (a+1)X aX X 0 (a+1)X 0 aX aX (a+1)X aX aX X 0 0 0 aX 0 X 0 0 0 X aX X aX (a+1)X (a+1)X 0 X (a+1)X 0 aX aX (a+1)X 0 X 0 aX (a+1)X X 0 aX 0 0 aX (a+1)X X aX 0 aX (a+1)X (a+1)X X aX 0 (a+1)X X (a+1)X X 0 (a+1)X aX X 0 X aX (a+1)X (a+1)X aX generates a code of length 51 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 144. Homogenous weight enumerator: w(x)=1x^0+261x^144+336x^146+645x^148+384x^150+654x^152+288x^154+417x^156+384x^158+369x^160+144x^162+183x^164+18x^168+3x^172+9x^176 The gray image is a linear code over GF(4) with n=204, k=6 and d=144. This code was found by Heurico 1.16 in 0.0827 seconds.