The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+14x^29+39x^30+7x^32+2x^37+1x^46

The gray image is a linear code over GF(2) with n=120, k=6 and d=58.
This code was found by Heurico 1.16 in 0.00637 seconds.