The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1  2  1 3X+2  1 3X  1  1  1  1  1  1  1  1  1  1 2X+2  1  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 X+3  1 2X+3  1 2X+1  1  2 3X  0 3X+2 2X X+2  2 2X+2 3X  X  2 3X+1 2X+3 3X+3  0
 0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0  0 2X  0 2X  0  0  0
 0  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X  0  0  0 2X  0 2X 2X 2X 2X 2X 2X  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+46x^34+260x^35+104x^36+244x^37+88x^38+204x^39+38x^40+28x^41+9x^42+1x^50+1x^56

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 0.031 seconds.