The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+178x^27+1129x^28+2200x^29+3830x^30+5798x^31+6616x^32+5784x^33+3891x^34+2022x^35+943x^36+240x^37+88x^38+34x^39+7x^40+7x^42

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 4.38 seconds.