The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  X  0  X  X
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X  2 X+2 X^2+2 X^2+X X^2+2  X  0 X^2+X X^2+2 X+2  2  0 X^2+2 X^2+X+2  X  2 X^2+2 X^2+X+2 X+2  2 X^2 X^2+X+2 X^2+X+2 X^2+X  X X^2+X+2 X^2+X
 0  0 X^2+2  0 X^2+2 X^2  0 X^2  2  2 X^2 X^2+2 X^2 X^2+2  2  2  0  0  0  2 X^2 X^2 X^2  2  0 X^2+2 X^2+2 X^2 X^2+2  2 X^2 X^2+2  0  2  0 X^2  0
 0  0  0  2  2  0  2  2  0  2  0  2  2  0  2  0  2  0  0  2  2  2  0  0  2  2  0  2  0  2  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+110x^34+16x^35+306x^36+224x^37+240x^38+16x^39+74x^40+34x^42+2x^44+1x^64

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 0.063 seconds.