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 0 1 1 1 X 1 1 1 1 1 1 1 1 1 1 4X 1 1 2X 1 1 1 1 1 1 1 1 1 3X 1 1 1 3X 2X 0 1 0 1 1 0 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 0 4X+2 X+3 2 3 4X+4 1 X+4 1 3 3X+4 4X 1 2 0 4X 3X+3 0 2X+3 2X+4 2X+1 2X+2 2X+3 1 2X+1 4X+4 1 X+1 0 4X+2 3X+4 4X+1 2X+3 2X+4 2X 2X+2 4X 3X X+3 X+1 1 3X 1 0 1 3X 2X+4 1 2X+4 4X+2 3X 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 X 4X+4 3X+1 4 2X 4X 3X+4 X+2 4X+1 2X+3 2X+4 2X+1 X+2 3X+4 X+2 3 2X+1 2X+2 2 3 4X+3 4X 3X 2X+1 2X+2 X+2 2X 2X+4 4X+3 2X+3 2X+1 X+3 4 3X+4 2X 4 1 3X+2 4 0 2X 1 X+4 3 2 4X 4X+4 1 2X+4 0 4X+4 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 2X+2 X+1 3X+1 X+2 3X+3 2X+3 4 2X+4 3X+3 3 2 2 3X 2X+3 4X 4X X 4X+3 2X+3 4X+1 2X+4 3X+2 4X+2 X 2X+3 4X+3 X+1 3 3X+4 3X+1 X+3 X X+4 X+4 X+1 4X X+1 1 1 3X+1 4X+4 X+4 4 3X+3 4X+3 X+3 X+1 2 2X+4 2X+3 4X+1 generates a code of length 89 over Z5[X]/(X^2) who´s minimum homogenous weight is 334. Homogenous weight enumerator: w(x)=1x^0+440x^334+1296x^335+1720x^336+1860x^337+1700x^338+3820x^339+5172x^340+5560x^341+5220x^342+4260x^343+8160x^344+11424x^345+10900x^346+7880x^347+6820x^348+12740x^349+15732x^350+14880x^351+10500x^352+9580x^353+18460x^354+22352x^355+18180x^356+13820x^357+11680x^358+20140x^359+23284x^360+18320x^361+12560x^362+10200x^363+15180x^364+16228x^365+12640x^366+8000x^367+4760x^368+7460x^369+6392x^370+4560x^371+2340x^372+920x^373+1100x^374+1192x^375+740x^376+320x^377+80x^378+28x^380+20x^385+4x^395 The gray image is a linear code over GF(5) with n=445, k=8 and d=334. This code was found by Heurico 1.16 in 370 seconds.