The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+153x^28+588x^29+1359x^30+1284x^31+1701x^32+1126x^33+1152x^34+516x^35+205x^36+60x^37+31x^38+8x^39+4x^40+2x^41+2x^42

The gray image is a code over GF(2) with n=256, k=13 and d=112.
This code was found by Heurico 1.16 in 0.282 seconds.