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 X^2  0 X^2  X  0 X^2  0  1  X  1  0  X  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  X  X  0 X^2  0  X X^2+X  X X^2  0 X^2+X  0  X  X X^2+X  X  X X^2  0  0  X X^2 X^2  X X^2+X
 0  0  X  0  X  X X^2+X  0  0  0  X  X  X  0 X^2 X^2+X X^2 X^2  0 X^2+X  0  X  X X^2+X  X X^2+X  X X^2+X X^2+X X^2+X X^2  X X^2 X^2  X X^2  X X^2+X
 0  0  0  X  X  0 X^2+X  X X^2  X X^2  0  X X^2 X^2+X  X  0  X X^2+X  X X^2 X^2+X  0  0 X^2+X X^2+X X^2  X X^2+X  0  X  0  X  X X^2+X  X X^2 X^2+X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  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 X^2  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+192x^30+403x^32+80x^33+623x^34+400x^35+1091x^36+544x^37+1459x^38+544x^39+1241x^40+400x^41+636x^42+80x^43+276x^44+148x^46+56x^48+13x^50+1x^52+1x^54+3x^56

The gray image is a linear code over GF(2) with n=152, k=13 and d=60.
This code was found by Heurico 1.16 in 24.1 seconds.