The generator matrix

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

generates a code of length 39 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+90x^33+1020x^34+2558x^35+5300x^36+7438x^37+10426x^38+11480x^39+10982x^40+7872x^41+5050x^42+1982x^43+892x^44+310x^45+110x^46+12x^47+9x^48+2x^49+2x^50

The gray image is a code over GF(2) with n=312, k=16 and d=132.
This code was found by Heurico 1.16 in 19.1 seconds.