The generator matrix

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

generates a code of length 29 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+46x^22+510x^23+1972x^24+6538x^25+14283x^26+31370x^27+46665x^28+58462x^29+47476x^30+32344x^31+14117x^32+5774x^33+1731x^34+650x^35+157x^36+26x^37+16x^38+6x^39

The gray image is a code over GF(2) with n=232, k=18 and d=88.
This code was found by Heurico 1.16 in 194 seconds.