The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 3X 1 1 1 1 1 1 1 2X X 1 1 4X 1 1 1 1 3X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4X 1 1 1 4X 1 1 1 1 1 1 1 1 3X 1 1 1 2X 0 1 0 0 X 2X 4X 1 3X+1 3X+4 2 3 3X+3 1 2 3X+2 3X+2 X+4 3X+4 3X+3 X+3 1 1 X+2 4X+4 1 4X+4 X+1 4X+3 3X+1 1 4X+3 2X 3X+2 X+1 X+4 4X+3 2X+2 X X+3 X+2 2X X+3 3X+3 4X+1 1 2X+1 0 2X+2 X 3X+1 3X+1 2X+2 4X 2 3 2X+1 X+1 3X X X+1 4X+3 1 0 0 1 1 3X+2 3 4 X+1 3X+3 3X+3 4X+3 4X+3 3X+4 4 4X 4X+1 2 4X+4 2X 3X+1 3X 3X+3 X+2 4X+4 3X+2 3X+1 1 2X+4 X+2 X+2 X+1 X+1 X+1 4X+1 X+3 X+4 X+3 3X+4 X+4 3X+3 3 2X+1 3X X 4X 2X+2 2X+2 4 4X+1 1 3X+2 3 X+4 3X+4 2X+1 X+4 4X+1 X+3 1 2X+1 2X+4 3 2X+4 0 0 0 3X 4X 2X 0 3X 3X 4X X 2X 0 3X 0 4X 2X 3X X X 2X 3X 2X X X 2X 0 2X 3X 4X 0 0 4X 3X X 0 4X 3X 2X 0 3X X X 4X 2X X 0 4X 0 4X 3X 0 4X 3X 2X X X 2X 3X 2X X 2X 0 generates a code of length 63 over Z5[X]/(X^2) who´s minimum homogenous weight is 236. Homogenous weight enumerator: w(x)=1x^0+1020x^236+500x^237+160x^238+540x^239+1328x^240+4140x^241+1420x^242+260x^243+1260x^244+2956x^245+8560x^246+2000x^247+520x^248+1580x^249+3636x^250+9900x^251+2240x^252+780x^253+2000x^254+4424x^255+10740x^256+1880x^257+540x^258+1520x^259+2580x^260+6760x^261+1420x^262+240x^263+600x^264+604x^265+1380x^266+540x^267+44x^270+20x^275+8x^280+12x^285+12x^295 The gray image is a linear code over GF(5) with n=315, k=7 and d=236. This code was found by Heurico 1.16 in 9.93 seconds.