The generator matrix

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

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+212x^29+257x^30+390x^31+402x^32+360x^33+206x^34+148x^35+26x^36+36x^37+1x^38+6x^39+3x^40

The gray image is a code over GF(2) with n=256, k=11 and d=116.
This code was found by Heurico 1.16 in 56.3 seconds.