The generator matrix

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

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+290x^35+84x^36+408x^37+16x^38+108x^39+24x^40+88x^41+2x^43+3x^48

The gray image is a code over GF(2) with n=296, k=10 and d=140.
This code was found by Heurico 1.16 in 10.2 seconds.