The generator matrix

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

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+350x^36+804x^37+813x^38+644x^39+501x^40+432x^41+273x^42+132x^43+98x^44+36x^45+9x^46+2x^48+1x^50

The gray image is a linear code over GF(2) with n=312, k=12 and d=144.
This code was found by Heurico 1.16 in 0.828 seconds.