The generator matrix

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

generates a code of length 32 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+238x^27+1136x^28+1934x^29+4304x^30+5344x^31+6722x^32+5684x^33+4284x^34+1782x^35+972x^36+222x^37+108x^38+28x^39+7x^40+2x^44

The gray image is a code over GF(2) with n=256, k=15 and d=108.
This code was found by Heurico 1.16 in 4.06 seconds.