The generator matrix

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

generates a code of length 38 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+18x^37+84x^38+18x^39+2x^41+1x^42+2x^43+1x^44+1x^50

The gray image is a code over GF(2) with n=304, k=7 and d=148.
This code was found by Heurico 1.16 in 0.015 seconds.