The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+65x^34+182x^35+202x^36+186x^37+171x^38+106x^39+69x^40+38x^41+3x^50+1x^54

The gray image is a code over GF(2) with n=296, k=10 and d=136.
This code was found by Heurico 1.16 in 0.046 seconds.