The generator matrix 1 0 0 0 1 1 1 1 1 1 1 1 2X 4X 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 X 1 2X 1 4X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2X 1 1 1 1 1 X 1 1 1 1 3X 1 1 1 1 1 1 1 1 0 1 X 4X 1 1 1 1 1 1 1 0 1 0 0 3X 4X 3X+1 4X+1 1 3X+2 4 3X+3 1 1 2X+4 X+4 1 2 4X+3 X+3 X+4 1 3X+4 X+1 4X+2 3X 2X+2 3X+1 2X+2 2X 2X+2 X+1 1 X+3 1 2X+3 1 2 X+3 2 4X+2 4X+1 4 X X+1 4 3X 2X+3 3 3X+4 0 4X 3X+3 4X 4 3X+4 X 1 4X 2X+4 X+1 4X+2 X+2 1 X 2X+2 2X 4X+3 1 2X+4 4X X+3 4X+2 4X+4 3X+1 0 3X+1 1 3X+4 1 4X 4 1 3X+3 0 4X+1 X+2 2X 0 0 1 0 3X+1 3X+2 3X+3 1 4X+2 X+1 2 2X+3 3X+2 2X+3 2X+1 X+3 X 4X+2 X+2 X+2 2X+3 X+1 3X 3X+4 4X 1 4X+3 0 3 3X+1 2X 4X+1 3 4X+1 4 2X+4 0 X+1 3X+1 4 4X+4 2 0 3X 4 3X+4 3 3X+2 2X+3 3X+4 4X 4X+4 X 4X+3 3 2 X 3X+1 4 4X+1 0 3 3X X X+3 3X+4 X+2 4 2 4X+2 3 4X+4 3X 2X+4 0 2 3 4X 3X+1 X+1 1 4X+1 3X+1 2X 4 X+2 2 X+2 0 0 0 1 3X+3 3X+2 4X+3 3X+1 X 4X+2 X+1 2X X+4 2 4 4X+4 3X 3X 1 X+2 2 X+4 4X+1 2X+1 3X+4 4X+2 X 2X+4 4 1 4X+1 X+3 2X+3 X+4 2X X+2 3X+4 3X+4 3X+1 X+2 X+1 4X+2 4X+2 3X+4 2X+4 3 4X+4 0 3 0 4X+3 2X+3 3 2X 2X+1 3X+4 X+2 4X+3 4X 2 2 3X+1 X 3X+2 X+1 2X+4 0 4 4X+2 3X+2 X+2 1 3 X+4 3X+3 4X+4 4X 3X+1 1 X+2 3 4X+3 0 4X+2 X+4 X+4 3 3X+3 generates a code of length 88 over Z5[X]/(X^2) who´s minimum homogenous weight is 330. Homogenous weight enumerator: w(x)=1x^0+680x^330+1380x^331+1480x^332+1460x^333+1580x^334+3940x^335+5820x^336+4680x^337+5240x^338+4420x^339+8424x^340+10940x^341+9700x^342+8180x^343+6880x^344+14036x^345+15500x^346+13900x^347+12140x^348+10360x^349+18964x^350+21260x^351+15600x^352+14160x^353+12740x^354+22180x^355+23440x^356+16400x^357+13380x^358+10940x^359+15716x^360+16260x^361+10980x^362+7880x^363+4980x^364+7716x^365+6700x^366+4140x^367+2320x^368+600x^369+1408x^370+1200x^371+620x^372+240x^373+24x^375+24x^380+8x^385+4x^390 The gray image is a linear code over GF(5) with n=440, k=8 and d=330. This code was found by Heurico 1.16 in 362 seconds.