The generator matrix

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

generates a code of length 45 over Z5[X]/(X^2) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+528x^165+440x^166+400x^167+180x^168+1440x^169+3464x^170+2000x^171+2280x^172+280x^173+3060x^174+6424x^175+3380x^176+3360x^177+880x^178+3780x^179+8416x^180+4460x^181+5840x^182+680x^183+4500x^184+8820x^185+3740x^186+3120x^187+480x^188+2220x^189+2884x^190+980x^191+24x^195+32x^200+16x^205+12x^210+4x^220

The gray image is a linear code over GF(5) with n=225, k=7 and d=165.
This code was found by Heurico 1.16 in 6.33 seconds.