The generator matrix

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

generates a code of length 39 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+113x^34+128x^35+368x^36+560x^37+449x^38+928x^39+431x^40+560x^41+298x^42+128x^43+79x^44+33x^46+13x^48+3x^50+3x^52+1x^56

The gray image is a linear code over GF(2) with n=312, k=12 and d=136.
This code was found by Heurico 1.16 in 0.266 seconds.