The generator matrix

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

generates a code of length 54 over Z5[X]/(X^2) who´s minimum homogenous weight is 197.

Homogenous weight enumerator: w(x)=1x^0+920x^197+1640x^198+1740x^199+1356x^200+1000x^201+4780x^202+6240x^203+6880x^204+4464x^205+2760x^206+11780x^207+13760x^208+14520x^209+8084x^210+6120x^211+21740x^212+24420x^213+24140x^214+12532x^215+10480x^216+34100x^217+33280x^218+27460x^219+13860x^220+9640x^221+26540x^222+22100x^223+16740x^224+6776x^225+2500x^226+7640x^227+6060x^228+3520x^229+980x^230+24x^235+20x^240+12x^245+4x^250+8x^255+4x^260

The gray image is a linear code over GF(5) with n=270, k=8 and d=197.
This code was found by Heurico 1.16 in 181 seconds.