The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+120x^23+581x^24+976x^25+1984x^26+2264x^27+3798x^28+3756x^29+5480x^30+3924x^31+4263x^32+2280x^33+1812x^34+832x^35+434x^36+156x^37+64x^38+28x^39+11x^40+4x^42

The gray image is a code over GF(2) with n=120, k=15 and d=46.
This code was found by Heurico 1.13 in 5.71 seconds.