The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X  1  1 X^3+X^2  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1 X^3  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X X^3+X^2+X+1 X^3+1  1 X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^3+X+1 X^3+X+1 X^3+X^2+1 X^2+X+1 X^3+X^2+1  1  X  X  1 X^2+X
 0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+215x^38+128x^39+140x^40+24x^42+1x^44+1x^46+1x^48+1x^60

The gray image is a linear code over GF(2) with n=312, k=9 and d=152.
This code was found by Heurico 1.16 in 41.3 seconds.