The generator matrix

 1  0  0  0  1  1  1 X^2+X  1  1  1  X  1 X^2  0  1  1  1  0  1 X^2+X  1  X  0  X  1 X^2+X  1  1  1
 0  1  0  0  0  1 X^2+X+1  1  X X+1  X  1 X^2+1  1  0 X^2+1 X^2 X+1  0 X^2+X+1  1 X^2+X  0  1 X^2 X^2+1  X X^2+X  0 X+1
 0  0  1  0  1  1  X X+1  1 X^2+1 X^2  1  0  0  1 X^2+X+1  X  0 X^2+X X^2+X X^2+X  0  1 X^2+X+1  1 X^2+X+1  1 X^2 X^2+1  X
 0  0  0  1  1  0 X^2  0 X^2 X^2+1 X+1 X^2+1 X^2+X+1  1 X^2+1  X X^2+1  X  1 X^2+X+1 X^2  0 X^2+X+1  X  X X^2 X^2+1 X^2 X+1  X
 0  0  0  0  X  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0  X X^2+X X^2+X X^2+X X^2+X  X X^2+X  X  X  X X^2+X X^2+X X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+168x^23+494x^24+1090x^25+1734x^26+2508x^27+3584x^28+4364x^29+4608x^30+4496x^31+3909x^32+2644x^33+1601x^34+876x^35+390x^36+220x^37+56x^38+16x^39+4x^40+2x^41+2x^44+1x^50

The gray image is a linear code over GF(2) with n=120, k=15 and d=46.
This code was found by Heurico 1.16 in 14.2 seconds.