The generator matrix

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

generates a code of length 42 over Z5[X]/(X^2) who´s minimum homogenous weight is 150.

Homogenous weight enumerator: w(x)=1x^0+788x^150+540x^151+1120x^152+1140x^153+3400x^154+5268x^155+4160x^156+4300x^157+4500x^158+8980x^159+12892x^160+10760x^161+10900x^162+10180x^163+20040x^164+25488x^165+22160x^166+19900x^167+17560x^168+31000x^169+36276x^170+28060x^171+21700x^172+15640x^173+22960x^174+21900x^175+11820x^176+7080x^177+3480x^178+3620x^179+2956x^180+32x^185+16x^190+8x^195

The gray image is a linear code over GF(5) with n=210, k=8 and d=150.
This code was found by Heurico 1.16 in 138 seconds.