The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+964x^32+2452x^33+5030x^34+7336x^35+10966x^36+11918x^37+11245x^38+7592x^39+4859x^40+1960x^41+904x^42+192x^43+72x^44+38x^45+5x^46+2x^48

The gray image is a code over GF(2) with n=296, k=16 and d=128.
This code was found by Heurico 1.16 in 448 seconds.