The generator matrix

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

generates a code of length 39 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+245x^32+1376x^33+4098x^34+9082x^35+18127x^36+30372x^37+43653x^38+47452x^39+44602x^40+30434x^41+18644x^42+8840x^43+3295x^44+1344x^45+421x^46+108x^47+30x^48+10x^49+6x^51+4x^52

The gray image is a code over GF(2) with n=312, k=18 and d=128.
This code was found by Heurico 1.16 in 303 seconds.