The generator matrix

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

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+56x^23+126x^24+242x^25+458x^26+600x^27+872x^28+1128x^29+1179x^30+1178x^31+933x^32+630x^33+381x^34+204x^35+108x^36+44x^37+29x^38+10x^39+8x^40+4x^41+1x^42

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 1.42 seconds.