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  X  2  X  X  1
 0  X  0 X^2+X+2  0 X^2+X  0 X+2 X^2 X^2+X X^2+2  X X^2 X^2+X+2 X^2  X  2 X^2+X+2  2 X^2+X  2 X^2+X  2 X^2+X+2 X^2+2 X+2 X^2+2 X+2 X^2+2 X+2 X^2  X X^2+X  X  2 X^2+X+2  0
 0  0 X^2+2 X^2  2 X^2+2 X^2  2 X^2  0  0 X^2 X^2+2  2  2 X^2+2  2 X^2+2 X^2  2 X^2+2 X^2  0  0 X^2+2 X^2+2  2  0 X^2 X^2  0  2  0 X^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 35.

Homogenous weight enumerator: w(x)=1x^0+30x^35+129x^36+196x^37+119x^38+30x^39+6x^40+1x^66

The gray image is a code over GF(2) with n=296, k=9 and d=140.
This code was found by Heurico 1.16 in 0.031 seconds.