The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+56x^11+72x^12+168x^13+50x^14+320x^15+91x^16+176x^17+12x^18+40x^19+28x^20+8x^21+2x^22

The gray image is a code over GF(2) with n=60, k=10 and d=22.
This code was found by Heurico 1.16 in 2.88 seconds.