The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+241x^26+1356x^27+3680x^28+8382x^29+15551x^30+22448x^31+26830x^32+23594x^33+16232x^34+7852x^35+3158x^36+1276x^37+323x^38+104x^39+27x^40+10x^41+5x^42+2x^45

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 58.6 seconds.