The generator matrix

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

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+28x^34+48x^35+23x^36+16x^37+792x^38+16x^39+23x^40+48x^41+28x^42+1x^76

The gray image is a linear code over GF(2) with n=304, k=10 and d=136.
This code was found by Heurico 1.16 in 0.031 seconds.