The generator matrix

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

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+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.