The generator matrix

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

generates a code of length 30 over Z5[X]/(X^2) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+620x^111+700x^112+720x^114+636x^115+2120x^116+1540x^117+960x^119+352x^120+1700x^121+1120x^122+1320x^124+612x^125+2060x^126+1140x^127+24x^130

The gray image is a linear code over GF(5) with n=150, k=6 and d=111.
This code was found by Heurico 1.16 in 0.152 seconds.