The generator matrix

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

generates a code of length 49 over Z5[X]/(X^2) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+980x^178+2480x^179+1708x^180+1380x^181+1840x^182+5320x^183+8180x^184+4916x^185+5280x^186+4480x^187+11980x^188+17960x^189+12000x^190+11040x^191+10120x^192+22680x^193+30060x^194+22568x^195+18700x^196+14960x^197+29880x^198+36160x^199+22452x^200+16460x^201+11600x^202+19800x^203+21880x^204+9364x^205+4640x^206+2000x^207+4360x^208+3280x^209+56x^210+32x^215+24x^220+4x^225

The gray image is a linear code over GF(5) with n=245, k=8 and d=178.
This code was found by Heurico 1.16 in 474 seconds.