The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+76x^29+105x^30+202x^31+314x^32+146x^33+76x^34+78x^35+12x^36+10x^37+3x^38+1x^56

The gray image is a code over GF(2) with n=256, k=10 and d=116.
This code was found by Heurico 1.16 in 0.031 seconds.