The generator matrix

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

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+120x^23+557x^24+1044x^25+1876x^26+2316x^27+3655x^28+4306x^29+5062x^30+3952x^31+4010x^32+2598x^33+1736x^34+828x^35+441x^36+174x^37+62x^38+16x^39+8x^40+6x^41

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 13.4 seconds.