The generator matrix

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

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+14x^37+102x^38+6x^40+2x^45+2x^46+1x^48

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 0.031 seconds.