The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+28x^22+38x^23+123x^24+244x^25+372x^26+636x^27+914x^28+1100x^29+1232x^30+1184x^31+913x^32+652x^33+376x^34+180x^35+84x^36+52x^37+36x^38+10x^39+11x^40+4x^42+2x^44

The gray image is a linear code over GF(2) with n=120, k=13 and d=44.
This code was found by Heurico 1.16 in 1.15 seconds.