The generator matrix

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

generates a code of length 29 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+84x^23+1124x^24+3020x^25+8040x^26+15138x^27+24194x^28+27508x^29+24730x^30+15330x^31+7903x^32+2676x^33+1020x^34+230x^35+58x^36+12x^37+2x^38+2x^39

The gray image is a code over GF(2) with n=232, k=17 and d=92.
This code was found by Heurico 1.16 in 51.1 seconds.