The generator matrix

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

generates a code of length 11 over Z5[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+140x^36+960x^37+464x^40+1120x^41+2880x^42+2000x^44+1628x^45+2240x^46+4160x^47+16x^50+16x^55

The gray image is a linear code over GF(5) with n=55, k=6 and d=36.
This code was found by Heurico 1.16 in 0.0351 seconds.