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

generates a code of length 30 over Z5[X]/(X^2) who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+160x^110+172x^115+2572x^120+76x^125+60x^130+40x^135+28x^140+8x^145+8x^150

The gray image is a linear code over GF(5) with n=150, k=5 and d=110.
This code was found by Heurico 1.16 in 0.0202 seconds.