The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 0 2 1 X 1 2 X 1 0 1 X X 1 2
0 X 0 X 0 0 X X+2 0 2 X 0 X X+2 X+2 2 X X 2 X+2 0 X X X X X X 2 0 X
0 0 X X 0 X+2 X 0 0 X X X+2 X+2 2 0 X 0 X X+2 0 2 X X 2 2 0 X+2 X X X
0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 2 0 2 2 2 2 0 0 2 0 0 2 2 2 2
0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 0 2 2 0 0 2 2 2 2 0 0 2 2
0 0 0 0 0 2 0 0 0 2 0 0 0 0 2 2 2 2 0 2 2 2 0 2 0 2 0 2 0 2
0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 0 2 2 2 2 2 2 0 0 2 0 2 0 2 0
0 0 0 0 0 0 0 2 0 2 2 2 2 0 2 0 2 2 0 2 0 0 0 2 0 0 0 0 2 2
0 0 0 0 0 0 0 0 2 0 0 2 0 2 2 2 0 2 0 0 2 0 0 2 2 2 2 0 2 0
generates a code of length 30 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 21.
Homogenous weight enumerator: w(x)=1x^0+16x^21+62x^22+126x^23+168x^24+364x^25+239x^26+948x^27+346x^28+1604x^29+425x^30+1600x^31+355x^32+1020x^33+238x^34+364x^35+132x^36+60x^37+56x^38+34x^39+20x^40+8x^41+3x^42+2x^44+1x^46
The gray image is a code over GF(2) with n=120, k=13 and d=42.
This code was found by Heurico 1.16 in 38 seconds.