The generator matrix

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

generates a code of length 11 over Z5[X]/(X^2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+212x^25+636x^30+1560x^35+3620x^40+62500x^44+4560x^45+3692x^50+1344x^55

The gray image is a linear code over GF(5) with n=55, k=7 and d=25.
This code was found by Heurico 1.16 in 1.18 seconds.