The generator matrix

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

generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+47x^32+24x^33+49x^34+108x^35+26x^36+468x^37+666x^38+368x^39+158x^40+16x^41+34x^42+28x^43+14x^44+4x^45+14x^46+8x^47+10x^48+4x^50+1x^66

The gray image is a linear code over GF(2) with n=304, k=11 and d=128.
This code was found by Heurico 1.16 in 0.093 seconds.