The generator matrix

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

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+184x^30+100x^32+400x^35+1500x^36+1200x^37+5520x^40+12000x^41+4800x^42+21020x^45+24000x^46+6400x^47+744x^50+256x^55

The gray image is a linear code over GF(5) with n=55, k=7 and d=30.
This code was found by Heurico 1.16 in 0.848 seconds.