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  X  X  X  1  1  X  X  1  1  1  X  1  1  X  X
 0 X^2  0  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 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  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2
 0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0
 0  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2
 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 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 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+62x^30+110x^32+88x^34+141x^36+1244x^38+183x^40+80x^42+47x^44+54x^46+25x^48+8x^50+3x^52+1x^56+1x^60

The gray image is a linear code over GF(2) with n=152, k=11 and d=60.
This code was found by Heurico 1.16 in 95.6 seconds.