The generator matrix

 1  0  1  1  1  0  1  1 X^2  1  1 X^2+X  1  1  0  1  1  X  1  1  1  0  0  1  1  1  1  1 X^2  0
 0  1  1  0 X+1  1 X^2+X+1  0  1 X^2 X^2+1  1  X X^2+X+1  1  1  0  1 X^2+X X+1  X  1  1 X^2+X X^2+1 X^2+X+1  1 X^2+1  X  1
 0  0  X  0  0  0  0  X  X X^2+X X^2+X X^2 X^2+X X^2+X X^2  0 X^2  0 X^2+X X^2+X X^2  0 X^2+X  0  X  X  0  0 X^2 X^2+X
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2  X X^2 X^2 X^2 X^2  X  X X^2+X X^2+X  X  0 X^2 X^2+X  0 X^2+X X^2 X^2 X^2 X^2+X  X
 0  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2
 0  0  0  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 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+60x^23+122x^24+204x^25+449x^26+694x^27+868x^28+1084x^29+1208x^30+1126x^31+941x^32+660x^33+366x^34+210x^35+106x^36+36x^37+24x^38+22x^39+8x^40+1x^42+2x^44

The gray image is a linear code over GF(2) with n=120, k=13 and d=46.
This code was found by Heurico 1.16 in 3.82 seconds.