The generator matrix

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

generates a code of length 38 over Z2[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+115x^30+239x^32+410x^34+806x^36+983x^38+784x^40+448x^42+168x^44+85x^46+48x^48+6x^50+2x^52+1x^54

The gray image is a linear code over GF(2) with n=152, k=12 and d=60.
This code was found by Heurico 1.16 in 9.65 seconds.