The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2X+2) 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 code over GF(2) with n=296, k=11 and d=132.
This code was found by Heurico 1.16 in 0.078 seconds.