The generator matrix 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 X 1 1 1 1 X 1 1 1 1 1 1 1 0 1 1 2 3X+4 3 0 3X+1 2 3X+4 3 1 0 3X+4 X 4X+4 3X+1 2 3 1 4X 2X+4 3X+1 X+2 1 X+3 2X+1 X+2 2X+3 1 4X+1 2X+2 2X 1 2X 2X+4 0 0 0 3X 0 3X 2X 0 4X 2X 4X X 3X 2X 0 3X 0 2X X 4X X 0 X 4X 2X 2X 4X 4X 2X 0 X 2X 0 4X 3X 2X 3X 0 0 0 0 X 3X X 2X 3X 0 2X 3X X 2X 3X X 4X 3X 2X X X X 0 2X X 4X 0 4X 4X 3X 0 2X 0 2X 2X 3X 4X X generates a code of length 37 over Z5[X]/(X^2) who´s minimum homogenous weight is 135. Homogenous weight enumerator: w(x)=1x^0+148x^135+160x^136+380x^138+720x^139+520x^140+380x^141+860x^143+840x^144+732x^145+600x^146+2140x^148+2160x^149+1004x^150+1020x^151+1620x^153+1280x^154+608x^155+340x^156+40x^160+12x^165+40x^170+12x^175+4x^180+4x^185 The gray image is a linear code over GF(5) with n=185, k=6 and d=135. This code was found by Heurico 1.16 in 0.247 seconds.