The generator matrix
1 1 X 1 1 1 1
0 2 2 0 0 2X 0
0 0 2X 0 2X 2X 0
0 0 0 2X 2X 0 0
generates a code of length 7 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+8x^4+40x^6+160x^7+37x^8+8x^10+2x^12
The gray image is a code over GF(2) with n=56, k=8 and d=16.
This code was found by Heurico 1.16 in -6.48e-008 seconds.