The generator matrix

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

generates a code of length 38 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+188x^34+272x^35+564x^36+624x^37+824x^38+624x^39+546x^40+272x^41+160x^42+7x^44+8x^46+4x^50+1x^52+1x^56

The gray image is a code over GF(2) with n=304, k=12 and d=136.
This code was found by Heurico 1.16 in 0.141 seconds.