The generator matrix

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

generates a code of length 33 over Z5[X]/(X^2) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+80x^111+220x^112+20x^113+180x^114+1024x^115+1060x^116+980x^117+1020x^118+2320x^119+6456x^120+4700x^121+3920x^122+4280x^123+7000x^124+17568x^125+12380x^126+12420x^127+11940x^128+16880x^129+38012x^130+25260x^131+25320x^132+22100x^133+26060x^134+49516x^135+27260x^136+20200x^137+13140x^138+12560x^139+17936x^140+6760x^141+1940x^142+48x^145+40x^150+12x^155+8x^160+4x^165

The gray image is a linear code over GF(5) with n=165, k=8 and d=111.
This code was found by Heurico 1.16 in 99.7 seconds.