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  2  1  1  1  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X+2 X^2+2 X^2+X+2  0 X+2 X^2+2  2 X^2+X X^2 X+2 X^2+X X^2+2 X+2  0  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2+X X^2  2  X X^2+X+2 X^2+2 X^2
 0  0  2  0  0  0  2  0  0  2  2  0  2  2  2  2  2  0  2  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  2  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  0  2  0  0  2  2  2  0  2  2  0  2  2  0  2  0  0  0  2  2  2  0  2
 0  0  0  0  2  2  2  2  2  0  2  0  2  0  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  0  2  2  2  0  2  0  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+89x^34+450x^36+410x^38+28x^40+45x^42+1x^72

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 0.093 seconds.