The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+506x^16+1288x^24+253x^28+12288x^30+253x^32+1288x^36+506x^44+1x^60

The gray image is a linear code over GF(2) with n=120, k=14 and d=32.
This code was found by Heurico 1.16 in 3.86 seconds.