The generator matrix

 1  0  0  1  1  1 2X+2  0 2X 2X+2  1  1  1  1 X+2  1 3X+2 3X  1  1  1  1  1  1 3X+2  1  1  1 X+2  0  1  2  1  X  X  0  1
 0  1  0  0  3  3  1 3X+2  1  1 2X 2X+3  2 X+3  X X+3  1  1 X+2 3X+1 2X+2  1 2X+2 X+1  1 3X X+2  2  1  1  1  1 3X  1 3X  1 2X+2
 0  0  1 X+1 3X+3 2X+2 3X+3  1 X+2  1 X+2 2X+1 2X+3  0  1 3X 3X+2 2X+3 2X 2X+1 2X+3 2X+2 X+1 3X+1 2X X+2 X+1  2  3 3X X+1 2X  1 3X+1  1  3  X
 0  0  0 2X 2X  0 2X 2X 2X  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0 2X  0 2X 2X 2X  0  0  0 2X  0  0  0 2X 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+206x^33+708x^34+1272x^35+1346x^36+1534x^37+1136x^38+1028x^39+462x^40+286x^41+168x^42+20x^43+14x^44+6x^45+4x^46+1x^48

The gray image is a code over GF(2) with n=296, k=13 and d=132.
This code was found by Heurico 1.16 in 0.359 seconds.