The generator matrix

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

generates a code of length 32 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+82x^25+626x^26+2752x^27+7237x^28+16538x^29+28745x^30+48732x^31+52285x^32+48696x^33+29824x^34+16704x^35+6497x^36+2490x^37+667x^38+180x^39+60x^40+18x^41+8x^42+2x^46

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 228 seconds.