The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+54x^25+692x^26+2858x^27+7014x^28+16006x^29+30426x^30+47202x^31+52442x^32+48656x^33+31143x^34+15466x^35+6596x^36+2678x^37+640x^38+182x^39+59x^40+14x^41+11x^42+4x^43

The gray image is a code over GF(2) with n=256, k=18 and d=100.
This code was found by Heurico 1.16 in 220 seconds.