The generator matrix

 1  0  0  1  1  1 X^3+X  X  1  1 X^3+X  1  1 X^3+X^2  1 X^2+X  1 X^2+X X^2  1  1  1 X^2+X  1  X  X  1  1  1  1  1  0 X^3+X X^3  1 X^2  1  1
 0  1  0  0 X^3+X^2+1 X+1  1 X^3  0 X^3+X+1  1 X^2+X X^3+1  1 X^3+X  1 X^3+X  1  1 X^3+1 X^3+X^2+X+1 X^3+X^2+X+1 X^2 X^2+X  1 X^2 X^2+X+1 X^3+X^2  X X^3 X+1  1 X^3+X X^2 X^2+1  X X^2  0
 0  0  1 X+1 X+1  0 X^2+X+1  1 X^3+X^2+X X^2+X+1 X^3+X X+1 X^2 X^2+1 X^3+X^2+1 X^3 X^3+X^2+X  1 X^3+X^2+X X^3+X+1 X^2+X X^2+X+1  1 X^3 X^3+X^2+X+1  1  1 X+1 X^2 X^3+X^2+1 X^2+X X^2+X+1  1  1 X^2+1  1  0  0
 0  0  0 X^2 X^3+X^2 X^3 X^2 X^2 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^2  0 X^3 X^2 X^3+X^2 X^3  0 X^2 X^3+X^2 X^2 X^3  0 X^2 X^3  0  0 X^2 X^3  0 X^3+X^2  0 X^2 X^2 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+114x^33+674x^34+1292x^35+2187x^36+2436x^37+3100x^38+2534x^39+2034x^40+1110x^41+638x^42+172x^43+49x^44+20x^45+12x^46+2x^47+7x^48+2x^52

The gray image is a linear code over GF(2) with n=304, k=14 and d=132.
This code was found by Heurico 1.16 in 2.36 seconds.