The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+374x^34+716x^35+714x^36+900x^37+460x^38+412x^39+246x^40+140x^41+106x^42+8x^43+14x^44+4x^46+1x^48

The gray image is a code over GF(2) with n=296, k=12 and d=136.
This code was found by Heurico 1.16 in 0.094 seconds.