The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X a^2*X  1
 0  1  0  1 a^2*X  0 a^2*X+a a^2 a^2*X+1 a^2*X+a^2 a*X+a a^2*X+a^2 a^2*X+1 X+a a^2*X+a a*X+a^2 a^2*X  1 a*X  1  1  0
 0  0  1 a^2  1  a X+a^2 a^2  a  0 a^2*X+1 X+a a*X a^2*X+1 X+a^2  X a*X+1 a*X+a  1 a*X+a^2 a^2*X+a  0
 0  0  0  X a^2*X a*X  X  0  X a*X  X a^2*X a*X  0 a*X  0  0 a^2*X  X a*X  0  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+225x^56+156x^57+432x^59+1524x^60+600x^61+624x^63+2952x^64+1008x^65+1296x^67+4035x^68+936x^69+720x^71+1455x^72+372x^73+30x^76+15x^80+3x^84

The gray image is a linear code over GF(4) with n=88, k=7 and d=56.
This code was found by Heurico 1.16 in 0.266 seconds.