The generator matrix

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

generates a code of length 38 over Z2[X]/(X^4) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+70x^33+61x^34+140x^35+148x^36+442x^37+377x^38+450x^39+123x^40+118x^41+31x^42+34x^43+12x^44+6x^45+11x^46+14x^47+3x^48+4x^49+2x^51+1x^56

The gray image is a linear code over GF(2) with n=304, k=11 and d=132.
This code was found by Heurico 1.16 in 4.88 seconds.