The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^2  0  1  0  1  X X^2  X  1  1  1  1  X  X  X X^2  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X  0 X^2+X X^2  X  X X^2  X  X X^2+X X^2 X^2+X X^2+X X^2 X^2  X  0 X^2  0  X  X  0
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X  0 X^2 X^2 X^2+X X^2  X X^2+X X^2  X  X  0 X^2+X  X X^2+X  X  0  0  X X^2 X^2+X  0
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2 X^2+X  X  0  0  0 X^2+X X^2 X^2+X  X  0 X^2 X^2  X X^2 X^2+X  X X^2+X  0  X  0
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 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+30x^30+62x^31+129x^32+172x^33+236x^34+348x^35+392x^36+462x^37+498x^38+442x^39+387x^40+338x^41+217x^42+146x^43+99x^44+50x^45+35x^46+24x^47+15x^48+2x^49+7x^50+2x^51+1x^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 0.576 seconds.