The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  X  2  1  1
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2 X^2+X+2 X^2+X  0  2  X X+2 X^2  0 X^2+X+2 X^2+2 X^2+X X^2  X X^2+X X+2 X^2  X X^2+2 X^2+2 X^2+X+2  X  2  2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X  2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X+2  0  2 X+2 X^2+X X^2  0 X+2 X^2+X X+2 X^2 X^2+X+2 X^2+2 X^2+X  X  X X^2 X+2  2

generates a code of length 37 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+68x^34+116x^35+159x^36+376x^37+146x^38+52x^39+71x^40+32x^41+2x^42+1x^68

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.