The generator matrix 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 X 1 X 1 1 1 1 0 1 1 1 4X 1 1 1 1 4X 1 1 1 1 2X 1 1 0 1 1 2 4 3 3X+1 0 2 3 1 3X+4 0 3 1 2 3X+1 3X+4 3 1 0 3X+1 3X+4 2 X X+2 3X+1 1 X+3 1 3X+2 4X+1 2X X+3 1 X 2 3X+4 1 4X+4 4X+3 3X+3 3X+3 1 3X+2 4X+4 X+2 3X+4 1 3X+1 0 0 0 3X 0 0 0 0 X 2X 3X X 4X 4X 4X 4X 0 3X 0 4X 4X 2X 2X X 3X 2X X 2X 0 0 4X 3X 3X 0 2X 2X X 2X 2X 3X 2X 0 3X 2X 3X 0 3X 2X X 3X 4X 0 0 0 0 X 0 X 3X 3X 0 X 4X 2X X X 3X 4X 0 X 3X 3X 4X 3X X X 2X 4X 0 X 2X 2X 0 3X 0 X 3X 3X 4X 3X 4X 4X 4X 4X 3X 2X 2X 4X 4X 4X 0 0 0 0 0 0 0 3X 3X 2X 4X 4X 3X 4X 3X 2X 0 X 4X 3X 4X 3X 2X 4X 3X 4X 0 0 X 2X X 4X 4X X 4X 2X 3X 2X X 0 4X 4X 2X 4X 3X X 3X X X 3X 0 0 0 0 generates a code of length 51 over Z5[X]/(X^2) who´s minimum homogenous weight is 180. Homogenous weight enumerator: w(x)=1x^0+56x^180+20x^182+300x^185+60x^186+420x^187+480x^188+480x^189+404x^190+320x^191+1340x^192+1960x^193+1180x^194+456x^195+1620x^196+3640x^197+3960x^198+2280x^199+388x^200+3120x^201+6540x^202+7560x^203+3780x^204+348x^205+4820x^206+8420x^207+7760x^208+3480x^209+300x^210+2560x^211+4620x^212+3280x^213+1300x^214+212x^215+280x^220+156x^225+136x^230+80x^235+4x^240+4x^245 The gray image is a linear code over GF(5) with n=255, k=7 and d=180. This code was found by Heurico 1.16 in 9.07 seconds.