The generator matrix

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

generates a code of length 11 over Z5[X]/(X^2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+180x^37+264x^40+540x^42+500x^44+828x^45+780x^47+16x^50+16x^55

The gray image is a linear code over GF(5) with n=55, k=5 and d=37.
This code was found by Heurico 1.16 in 0.00212 seconds.