The generator matrix

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

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+36x^23+109x^24+118x^25+241x^26+166x^27+688x^28+198x^29+951x^30+206x^31+667x^32+146x^33+276x^34+98x^35+62x^36+50x^37+36x^38+6x^39+7x^40+3x^42+2x^44+1x^46

The gray image is a linear code over GF(2) with n=120, k=12 and d=44.
This code was found by Heurico 1.16 in 0.394 seconds.