The generator matrix

 1  0  1  1  1  2 X^2+X  1  1  1 X^2+X+2  1  1  1  1 X^2+2  1  X  1  1 X+2  1  1 X^2  1  1  1  1  1  1  1  X  1  1  1  0  1
 0  1 X+1 X^2+X+2 X^2+1  1  1  2 X^2+3 X^2+X  1 X^2+X+1  3 X+1 X^2+2  1  X  1 X+2  1  1 X^2 X^2+X+3  1  0 X^2+X+2 X^2+X+2  X  0 X^2+2 X^2+2  2 X^2+X X+3 X+3 X^2  0
 0  0 X^2 X^2+2  2 X^2  0 X^2 X^2+2  0 X^2+2 X^2+2  2  0  2  2 X^2+2 X^2+2  2 X^2  2 X^2  0 X^2  2 X^2  2  0 X^2 X^2+2  0  0 X^2+2 X^2+2 X^2 X^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+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 0.031 seconds.