The generator matrix

 1  0  0  1  1  1  2 X^2  1  1  0  1  1  0  X  1  1 X^2+X  1  1 X+2 X^2+X+2  1 X^2+X+2  1 X^2  1  1  1 X+2  1 X^2  1  0  1  1  1  1
 0  1  0  0 X^2+3 X^2+3  1  X  2 X^2+1  1  2 X^2+1  1  1  X X+1  1 X^2+X+2 X^2+X+3 X^2+X+2 X^2 X^2+X  1 X^2+X+3  1 X+1  1  X  1 X^2  1 X+3  1 X^2+X  1 X^2+X  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^2+X+2  3  3 X^2+3 X+2 X^2+X  X  X  2  1 X^2+X+1 X+3  1  1  1 X^2+X+3 X^2+1  1 X^2+X+2 X^2+2  2 X+1 X+1 X^2 X^2+X X^2+X+2  1 X^2+X+2  X  0
 0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  2  0  0  0  2  2  0  0  2  0  2  2  0  2  0  2  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+245x^34+784x^35+1063x^36+1432x^37+1475x^38+1284x^39+867x^40+600x^41+255x^42+88x^43+53x^44+32x^45+9x^46+4x^47

The gray image is a code over GF(2) with n=304, k=13 and d=136.
This code was found by Heurico 1.16 in 0.312 seconds.