The generator matrix

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

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+80x^32+480x^33+136x^35+1200x^36+960x^37+2160x^38+3116x^40+9600x^41+3840x^42+6240x^43+7500x^44+12156x^45+19200x^46+5120x^47+6120x^48+160x^50+56x^55

The gray image is a linear code over GF(5) with n=55, k=7 and d=32.
This code was found by Heurico 1.16 in 0.795 seconds.