The generator matrix

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

generates a code of length 32 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+199x^26+1320x^27+3778x^28+8758x^29+14553x^30+23532x^31+26106x^32+24516x^33+14834x^34+8450x^35+3418x^36+1174x^37+329x^38+72x^39+7x^40+16x^41+5x^42+2x^43+2x^44

The gray image is a code over GF(2) with n=256, k=17 and d=104.
This code was found by Heurico 1.16 in 56.9 seconds.