The generator matrix

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

generates a code of length 38 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+116x^33+727x^34+1278x^35+1960x^36+2704x^37+2853x^38+2834x^39+1998x^40+1036x^41+541x^42+206x^43+100x^44+14x^45+7x^46+2x^47+5x^48+2x^53

The gray image is a code over GF(2) with n=304, k=14 and d=132.
This code was found by Heurico 1.16 in 1.33 seconds.