The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  0  1 X^2  X  1 X^2 X^2  X  X  1  1  X  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  0  0  0  X X^2+X  X X^2  X  X  X X^2  X  0  0 X^2+X X^2  0
 0  0  X  0  X  X X^2+X  0  0  0  X  X X^2+X X^2  X  X X^2 X^2  0 X^2  0  0  0  X X^2+X  X X^2+X  X  0  X
 0  0  0  X  X  0 X^2+X  X X^2  X X^2  0 X^2+X X^2+X  X X^2+X X^2  0  X X^2+X  0  X X^2+X  0  0 X^2+X  X X^2+X X^2  X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 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+69x^22+96x^23+190x^24+314x^25+261x^26+854x^27+330x^28+1810x^29+348x^30+1790x^31+347x^32+878x^33+268x^34+322x^35+142x^36+70x^37+71x^38+10x^39+12x^40+7x^42+2x^48

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 1.68 seconds.