The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 X 1 1 a*X 0 1 1 1 a*X 1 1 1 a^2*X 1 1 1 1 1 1 1 X 1 1 1 1 a*X 1 1 1 1 1 1 1 1 1 1 a^2*X 1 0 a*X 1 1 1 1 1 1 0 1 1 1 1 1 1 1 a^2*X 1 1 1 1 1 1 1 1 a^2*X 1 1 0 1 0 0 a^2*X a*X a^2*X X X X 1 1 1 a a^2*X+a^2 a^2*X+a 1 X+1 a^2*X+1 1 1 a*X+a^2 a^2*X+a a^2*X 1 1 a^2*X+a^2 a^2 1 X+a 1 X+1 a*X+1 a^2 a*X+1 a*X+a^2 0 a*X+a a a^2*X+a^2 0 1 a^2 X+a a^2*X+a X a*X+1 a X+a 0 a^2*X X+1 1 1 1 0 0 a*X a^2 a*X+a^2 a*X+a^2 X+a^2 1 a a*X+a^2 1 a*X X+a^2 a*X+a X a*X a*X+1 a a*X a*X a^2*X+1 a a*X+a X+a^2 1 a^2*X+1 X 0 0 1 0 0 X X a^2*X+1 a a^2*X+a^2 a*X 0 a*X a*X X+1 a*X+a^2 a*X+1 X+a X+a X+1 X+a X+a^2 a^2*X+a a*X+a^2 a^2*X a*X+1 a*X+1 a^2*X+a^2 X+a^2 X a^2 a*X+a X+a^2 a^2*X+1 a^2*X+1 a 1 a^2*X+a^2 X a*X+a a*X+1 a*X+a^2 a X+1 a*X X+a 0 X+a a^2 a 1 a^2*X+1 a^2*X+1 X+1 a*X+a 1 X+a^2 X+a^2 a^2*X a^2*X X a*X+1 1 a^2*X a^2*X+a^2 a^2*X+a a^2*X+1 X a^2*X+1 a*X+a 1 a^2*X+a^2 a^2*X+a^2 0 1 1 a*X+a X a^2*X+1 a*X+a X+a^2 X+a^2 0 0 0 1 1 a^2*X+a a^2*X+a^2 a^2 X+a^2 a*X+a^2 a^2*X+a^2 X+1 a X a^2*X 1 0 X+a^2 a*X+a a^2*X+a^2 a*X a*X a*X+a X+1 1 a^2 X+a a a^2*X+a^2 a^2 a^2*X+1 a*X X+a X+1 1 a^2*X+1 a^2 a^2*X+a a*X+a a^2 1 a^2*X+a X+a X+1 a*X+1 X+a a^2*X a^2*X+a^2 a*X+a^2 X+1 a*X+a X+a a^2*X+1 a*X a^2*X+a^2 a^2*X+a X a*X+a X a^2*X+a a*X+1 a^2*X+a a^2*X+a a^2*X+1 a^2*X+a^2 a*X+1 X a^2*X+a^2 a^2*X a^2*X+1 a^2*X X X+a^2 a*X+a^2 a^2*X+a^2 a^2*X+1 a*X+1 a a^2 a^2 0 a*X+1 generates a code of length 82 over F4[X]/(X^2) who´s minimum homogenous weight is 230. Homogenous weight enumerator: w(x)=1x^0+636x^230+684x^231+639x^232+516x^233+2628x^234+1776x^235+1620x^236+816x^237+3504x^238+2964x^239+2118x^240+972x^241+4716x^242+3216x^243+2478x^244+1008x^245+4608x^246+2856x^247+2256x^248+1116x^249+4932x^250+3240x^251+2004x^252+948x^253+3696x^254+2112x^255+1269x^256+456x^257+1992x^258+1212x^259+714x^260+252x^261+840x^262+360x^263+213x^264+60x^265+84x^266+12x^267+12x^270 The gray image is a linear code over GF(4) with n=328, k=8 and d=230. This code was found by Heurico 1.16 in 26.6 seconds.