The generator matrix

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

generates a code of length 29 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+58x^22+558x^23+2065x^24+6106x^25+14602x^26+31008x^27+47159x^28+58438x^29+47618x^30+31796x^31+14368x^32+5664x^33+1966x^34+538x^35+149x^36+30x^37+12x^38+2x^39+2x^40+2x^41+2x^43

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 190 seconds.