The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+188x^31+968x^32+2902x^33+4212x^34+8152x^35+9791x^36+12800x^37+10319x^38+8234x^39+4223x^40+2538x^41+732x^42+336x^43+81x^44+48x^45+7x^46+2x^47+2x^50

The gray image is a code over GF(2) with n=296, k=16 and d=124.
This code was found by Heurico 1.16 in 19.3 seconds.