The generator matrix

 1  0  1  1  1  1  1  1  1  1  1
 0  1 3X+1  2 3X+4  3  X 4X+1 X+2 4X+4 2X

generates a code of length 11 over Z5[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+44x^40+120x^41+60x^42+172x^45+180x^46+40x^47+8x^50

The gray image is a linear code over GF(5) with n=55, k=4 and d=40.
This code was found by Heurico 1.16 in 0.000259 seconds.