The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+120x^24+310x^25+481x^26+606x^27+1068x^28+818x^29+1345x^30+974x^31+983x^32+650x^33+451x^34+170x^35+124x^36+46x^37+27x^38+10x^39+8x^40

The gray image is a linear code over GF(2) with n=120, k=13 and d=48.
This code was found by Heurico 1.16 in 1.19 seconds.