The generator matrix

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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+74x^36+48x^38+256x^39+89x^40+16x^42+22x^44+5x^48+1x^56

The gray image is a linear code over GF(2) with n=312, k=9 and d=144.
This code was found by Heurico 1.16 in 0.172 seconds.