The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1  a a^2*X+a^2  0 a^2*X+1  a a^2*X+a^2  1  0  a a^2*X+1 a^2*X+a^2  X a*X+a^2  X X+a^2 X+a a^2*X+a  0  X
 0  0 a^2*X  0  X  0  X a*X a*X a*X a*X  X a^2*X a^2*X a^2*X  0  X a^2*X  0 a*X a^2*X a^2*X
 0  0  0  X a*X a*X  0 a*X  X  X  0  X a*X  X  0 a^2*X a^2*X a^2*X  0 a^2*X a^2*X a*X

generates a code of length 22 over F4[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+21x^56+60x^57+216x^59+102x^60+288x^61+312x^63+363x^64+504x^65+648x^67+474x^68+576x^69+360x^71+21x^72+108x^73+18x^76+18x^80+6x^84

The gray image is a linear code over GF(4) with n=88, k=6 and d=56.
This code was found by Heurico 1.16 in 0.0259 seconds.