The generator matrix

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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+130x^35+397x^36+554x^37+703x^38+702x^39+669x^40+428x^41+250x^42+130x^43+77x^44+34x^45+6x^46+6x^47+8x^48+1x^54

The gray image is a linear code over GF(2) with n=312, k=12 and d=140.
This code was found by Heurico 1.16 in 0.141 seconds.