The generator matrix

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

generates a code of length 11 over Z5[X]/(X^2) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+180x^30+420x^35+2980x^40+11060x^45+724x^50+260x^55

The gray image is a linear code over GF(5) with n=55, k=6 and d=30.
This code was found by Heurico 1.16 in 0.0755 seconds.