The generator matrix

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

generates a code of length 51 over Z5[X]/(X^2) who´s minimum homogenous weight is 189.

Homogenous weight enumerator: w(x)=1x^0+240x^189+1088x^190+760x^191+580x^192+1260x^193+2260x^194+3696x^195+2040x^196+1320x^197+2460x^198+3640x^199+5800x^200+3540x^201+1780x^202+3060x^203+4620x^204+6604x^205+5140x^206+2340x^207+3960x^208+4600x^209+5700x^210+3140x^211+1300x^212+1760x^213+2140x^214+2652x^215+380x^216+180x^217+32x^220+12x^225+24x^230+8x^235+8x^240

The gray image is a linear code over GF(5) with n=255, k=7 and d=189.
This code was found by Heurico 1.16 in 7.57 seconds.