The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+66x^20+42x^21+185x^22+260x^23+324x^24+734x^25+657x^26+1354x^27+1675x^28+1684x^29+2321x^30+1688x^31+1731x^32+1436x^33+746x^34+740x^35+248x^36+194x^37+155x^38+52x^39+48x^40+6x^41+29x^42+2x^43+3x^44+3x^46

The gray image is a linear code over GF(2) with n=120, k=14 and d=40.
This code was found by Heurico 1.16 in 5.57 seconds.