The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 (a+1)X 1 1 1 1 aX 1 1 1 1 1 1 aX 1 X 1 1 1 1 1 1 1 1 1 1 0 1 1 1 aX 1 X (a+1)X 1 1 (a+1)X 1 1 1 1 aX 1 0 1 1 1 1 1 1 0 1 1 0 aX 1 1 1 1 1 aX 0 1 1 1 1 1 1 0 1 0 0 (a+1)X 0 (a+1)X 1 (a+1)X+a a+1 X 0 X X X+a X+1 X+a+1 1 a a+1 a X+a+1 aX+a a+1 1 (a+1)X 1 X+a aX+1 X+a+1 a+1 X+1 aX+a+1 (a+1)X+a (a+1)X (a+1)X+a+1 X+a 1 1 X+a+1 aX+a+1 1 aX 0 1 X (a+1)X+1 1 aX+a aX+1 aX+a a 1 X+1 1 0 1 X (a+1)X+a (a+1)X+a+1 X+1 1 (a+1)X+1 aX+a+1 1 X a 1 aX+a 0 a+1 1 X (a+1)X+1 X+1 aX+a+1 X+1 1 aX 0 0 1 0 X aX 0 (a+1)X (a+1)X (a+1)X (a+1)X+1 (a+1)X+1 1 a X+1 a+1 a aX+a+1 (a+1)X+a 1 aX+a X+1 a+1 aX+a+1 a aX+1 (a+1)X+1 X aX+a X+a+1 (a+1)X+a 0 (a+1)X+1 X+a aX+a+1 X a+1 aX+a+1 1 X (a+1)X+a+1 X+1 X+a 1 X+1 a+1 aX 0 (a+1)X a (a+1)X+a (a+1)X+1 X+a (a+1)X+1 aX (a+1)X+a+1 X+1 1 0 a a a (a+1)X (a+1)X+1 aX+a 1 aX+1 1 X+a+1 X+a+1 aX (a+1)X+1 1 X aX+a+1 aX+a 1 a 0 0 0 0 1 (a+1)X+1 a a+1 (a+1)X+a+1 X+a+1 aX+a+1 a+1 X+a (a+1)X+1 1 X (a+1)X+a+1 X+a+1 a X+a+1 a+1 (a+1)X X+1 aX (a+1)X+a+1 X aX (a+1)X+a a aX+1 X 0 X+a a X+a X+1 aX+1 (a+1)X+a aX+1 (a+1)X+1 (a+1)X (a+1)X+a a+1 aX+a (a+1)X+a 1 a (a+1)X a+1 X+1 X (a+1)X+1 X+1 (a+1)X+1 X 1 X+a+1 a aX+1 aX (a+1)X+a aX+a+1 aX+a+1 aX+1 X X+a aX+a+1 aX+a+1 aX+a+1 1 (a+1)X+1 aX+a X+a 1 X+1 aX+1 X+1 aX+a 1 X+a+1 generates a code of length 79 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 221. Homogenous weight enumerator: w(x)=1x^0+516x^221+888x^222+936x^223+594x^224+1680x^225+1896x^226+1716x^227+684x^228+3060x^229+3192x^230+2316x^231+1401x^232+3720x^233+3672x^234+2484x^235+1332x^236+3732x^237+4128x^238+3048x^239+1305x^240+3528x^241+3672x^242+2352x^243+930x^244+3012x^245+2376x^246+1668x^247+507x^248+1728x^249+1224x^250+732x^251+360x^252+432x^253+456x^254+96x^255+48x^256+96x^257+12x^259+6x^260 The gray image is a linear code over GF(4) with n=316, k=8 and d=221. This code was found by Heurico 1.16 in 60.7 seconds.