The generator matrix

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

generates a code of length 11 over Z5[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+740x^32+2560x^33+128x^35+2700x^36+8880x^37+11520x^38+24148x^40+21600x^41+35520x^42+33280x^43+30000x^44+96108x^45+43200x^46+47360x^47+32640x^48+192x^50+48x^55

The gray image is a linear code over GF(5) with n=55, k=8 and d=32.
This code was found by Heurico 1.16 in 17.7 seconds.