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

generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+80x^34+392x^35+573x^36+808x^37+692x^38+596x^39+437x^40+284x^41+108x^42+68x^43+20x^44+28x^45+8x^46+1x^52

The gray image is a linear code over GF(2) with n=304, k=12 and d=136.
This code was found by Heurico 1.16 in 0.141 seconds.