The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+90x^33+198x^34+208x^35+449x^36+200x^37+442x^38+180x^39+175x^40+74x^41+6x^42+8x^43+5x^44+4x^45+2x^46+4x^47+1x^48+1x^56

The gray image is a linear code over GF(2) with n=296, k=11 and d=132.
This code was found by Heurico 1.16 in 0.078 seconds.