The generator matrix
1 1 1 1 1 1 1 1 1 X X X 1 0 1
0 X 0 0 0 X X+2 X 2 0 X 2 X 0 0
0 0 X 0 X X X 0 2 0 X+2 X+2 X X 0
0 0 0 X X 0 X X+2 0 X+2 2 X 2 0 0
0 0 0 0 2 0 0 0 2 2 2 2 0 2 0
0 0 0 0 0 2 0 2 0 2 0 2 0 2 2
generates a code of length 15 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+42x^10+76x^11+115x^12+244x^13+351x^14+376x^15+366x^16+264x^17+109x^18+60x^19+29x^20+4x^21+9x^22+1x^24+1x^26
The gray image is a code over GF(2) with n=60, k=11 and d=20.
This code was found by Heurico 1.16 in 0.0295 seconds.