The generator matrix

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

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+80x^34+392x^35+573x^36+808x^37+692x^38+596x^39+437x^40+284x^41+108x^42+68x^43+20x^44+28x^45+8x^46+1x^52

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.