The generator matrix

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

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+60x^40+500x^44+40x^45+4x^50+20x^55

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 0.000384 seconds.