The generator matrix

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

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+150x^23+544x^24+976x^25+1804x^26+2628x^27+3604x^28+4244x^29+4408x^30+4714x^31+3819x^32+2696x^33+1660x^34+810x^35+473x^36+148x^37+64x^38+16x^39+4x^40+2x^43+2x^44+1x^52

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 42.2 seconds.