The generator matrix

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

generates a code of length 35 over Z5[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+84x^110+460x^115+952x^120+1160x^125+1660x^130+2500x^132+1952x^135+20000x^137+2296x^140+40000x^142+2468x^145+2160x^150+1440x^155+744x^160+184x^165+60x^170+4x^175

The gray image is a linear code over GF(5) with n=175, k=7 and d=110.
This code was found by Heurico 1.16 in 11.2 seconds.