The generator matrix

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

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+188x^34+272x^35+564x^36+624x^37+824x^38+624x^39+546x^40+272x^41+160x^42+7x^44+8x^46+4x^50+1x^52+1x^56

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 0.156 seconds.