The generator matrix

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

generates a code of length 30 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+90x^23+834x^24+2444x^25+7188x^26+15914x^27+31157x^28+45454x^29+55167x^30+46662x^31+31323x^32+15396x^33+7214x^34+2358x^35+709x^36+174x^37+27x^38+16x^39+8x^40+4x^41+4x^42

The gray image is a code over GF(2) with n=240, k=18 and d=92.
This code was found by Heurico 1.16 in 209 seconds.