The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2) 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 0.031 seconds.