The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+220x^29+962x^30+504x^31+1052x^32+308x^33+644x^34+204x^35+138x^36+32x^37+18x^38+12x^39+1x^40

The gray image is a code over GF(2) with n=256, k=12 and d=116.
This code was found by Heurico 1.16 in 0.078 seconds.