The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 (a+1)X 1 1 1 1 (a+1)X 1 1 aX 1 1 1 1 1 1 1 1 1 1 (a+1)X X 1 1 1 0 1 (a+1)X 1 1 X 1 1 1 1 1 aX 1 1 aX 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1 1 1 0 1 0 0 0 (a+1)X 1 (a+1)X+a a+1 (a+1)X+1 1 (a+1)X+a (a+1)X+a+1 (a+1)X+a+1 1 1 a (a+1)X+1 a+1 a 1 aX X+a+1 1 1 (a+1)X+a X+a+1 X+a+1 (a+1)X aX+1 aX+a aX 0 1 0 1 (a+1)X+a aX+a+1 1 1 0 1 (a+1)X+a+1 aX 1 (a+1)X (a+1)X+a+1 aX+a+1 (a+1)X+a aX 1 a+1 X+a 1 aX aX+1 X+a+1 aX+a aX+a+1 X+1 X X+1 a (a+1)X+a+1 aX+a 1 aX+1 X a+1 0 a 0 0 0 1 1 a a+1 1 X+1 1 0 a+1 X+a+1 aX a a 1 aX+a a a+1 X a+1 X+1 aX+a (a+1)X X+1 1 (a+1)X+a+1 aX+1 0 (a+1)X+a+1 X+a (a+1)X+a X+a+1 (a+1)X+a 1 (a+1)X+a+1 aX+a+1 X (a+1)X (a+1)X+a aX+a aX+1 a+1 X aX+1 aX X X+a aX+a+1 (a+1)X+a+1 X+a 1 a a aX+a (a+1)X+a+1 X+a aX+a+1 X+a+1 X+1 X+1 X+a 1 aX+a (a+1)X (a+1)X+a 0 1 aX+a+1 X+1 aX X 0 0 0 (a+1)X 0 0 0 aX aX aX (a+1)X X X X X (a+1)X (a+1)X aX (a+1)X X aX X X 0 X 0 0 (a+1)X aX X (a+1)X 0 aX X 0 0 aX 0 aX aX aX (a+1)X aX (a+1)X X (a+1)X 0 aX X (a+1)X X X 0 (a+1)X aX aX 0 aX 0 0 0 aX (a+1)X 0 (a+1)X 0 (a+1)X X X X aX 0 0 0 0 0 X aX (a+1)X X 0 aX X (a+1)X X 0 X (a+1)X aX 0 aX 0 X (a+1)X aX (a+1)X X X 0 (a+1)X (a+1)X aX X 0 0 aX (a+1)X (a+1)X (a+1)X (a+1)X (a+1)X 0 X 0 (a+1)X X X 0 0 X X (a+1)X 0 aX (a+1)X 0 (a+1)X aX (a+1)X aX X X (a+1)X (a+1)X 0 X aX X 0 aX (a+1)X X 0 aX generates a code of length 72 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 199. Homogenous weight enumerator: w(x)=1x^0+240x^199+516x^200+228x^201+420x^202+1860x^203+1401x^204+960x^205+900x^206+2988x^207+2553x^208+1248x^209+1536x^210+4284x^211+3246x^212+1644x^213+1632x^214+5460x^215+3963x^216+1680x^217+1848x^218+5520x^219+3393x^220+1752x^221+1668x^222+4404x^223+2712x^224+1296x^225+864x^226+2220x^227+1170x^228+348x^229+312x^230+636x^231+342x^232+60x^233+36x^234+36x^235+63x^236+39x^240+36x^244+15x^248+3x^252+3x^256 The gray image is a linear code over GF(4) with n=288, k=8 and d=199. This code was found by Heurico 1.16 in 22.6 seconds.