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.