The generator matrix

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

generates a code of length 56 over Z5[X]/(X^2) who´s minimum homogenous weight is 214.

Homogenous weight enumerator: w(x)=1x^0+360x^214+1552x^215+720x^216+420x^217+1080x^219+1916x^220+760x^221+520x^222+840x^224+1640x^225+740x^226+260x^227+640x^229+1508x^230+560x^231+140x^232+580x^234+1000x^235+220x^236+160x^237+8x^245

The gray image is a linear code over GF(5) with n=280, k=6 and d=214.
This code was found by Heurico 1.16 in 16.4 seconds.