The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  1  1  1  1
 0  X  0  X  0  0  X X+2  X X+2  2  2 X+2  2  X
 0  0  X  X  0 X+2  X  0  X  0  X  X  X X+2 X+2
 0  0  0  2  0  0  0  2  0  0  2  2  2  0  2
 0  0  0  0  2  0  0  0  0  2  2  2  0  2  0
 0  0  0  0  0  2  0  0  2  2  0  0  2  2  0
 0  0  0  0  0  0  2  2  2  0  0  2  0  0  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+73x^10+167x^12+192x^13+265x^14+640x^15+288x^16+192x^17+163x^18+53x^20+11x^22+3x^24

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 8.95 seconds.