The generator matrix

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

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+352x^34+784x^35+696x^36+784x^37+536x^38+472x^39+227x^40+96x^41+96x^42+40x^43+10x^44+2x^48

The gray image is a code over GF(2) with n=296, k=12 and d=136.
This code was found by Heurico 1.16 in 0.094 seconds.