The generator matrix

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

generates a code of length 47 over Z5[X]/(X^2) who´s minimum homogenous weight is 178.

Homogenous weight enumerator: w(x)=1x^0+840x^178+520x^179+224x^180+480x^181+280x^182+2100x^183+1320x^184+336x^185+660x^186+340x^187+2000x^188+980x^189+244x^190+440x^191+280x^192+1340x^193+800x^194+296x^195+420x^196+100x^197+1220x^198+380x^199+8x^200+8x^205+4x^210+4x^215

The gray image is a linear code over GF(5) with n=235, k=6 and d=178.
This code was found by Heurico 1.16 in 0.264 seconds.