The generator matrix 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 X 1 X 1 1 1 1 1 3X 1 1 1 1 1 0 1 1 2 3X+4 3 0 3X+1 2 3X+4 3 1 0 3X+4 3 1 3X+1 2 X+3 1 X+3 1 X X X X+3 4X+3 1 2X 3X+3 2X X+2 0 0 0 3X 0 3X 2X 0 4X 2X 4X X 3X 2X 0 3X 3X 3X 0 2X X X 0 0 4X 3X 2X X 3X 4X 4X X 3X 3X 0 0 0 X 3X X 2X 3X 0 2X 3X X 2X 3X X 3X 4X 2X 3X 4X 2X 4X X 2X 0 0 0 4X 0 X X X 0 generates a code of length 33 over Z5[X]/(X^2) who´s minimum homogenous weight is 120. Homogenous weight enumerator: w(x)=1x^0+308x^120+280x^121+360x^123+1120x^125+920x^126+420x^128+2500x^130+1660x^131+1080x^133+3600x^135+1800x^136+640x^138+476x^140+340x^141+52x^145+44x^150+20x^155+4x^165 The gray image is a linear code over GF(5) with n=165, k=6 and d=120. This code was found by Heurico 1.16 in 0.21 seconds.