The generator matrix

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

generates a code of length 37 over Z5[X]/(X^2) who´s minimum homogenous weight is 125.

Homogenous weight enumerator: w(x)=1x^0+68x^125+80x^127+252x^130+180x^131+360x^132+80x^133+540x^134+400x^135+1520x^136+1000x^137+680x^138+1840x^139+424x^140+3320x^141+2000x^142+2480x^143+6240x^144+440x^145+7120x^146+3200x^147+5180x^148+9840x^149+412x^150+8820x^151+3820x^152+4080x^153+6540x^154+340x^155+4040x^156+2040x^157+340x^160+256x^165+140x^170+44x^175+8x^180

The gray image is a linear code over GF(5) with n=185, k=7 and d=125.
This code was found by Heurico 1.16 in 5.88 seconds.