The generator matrix

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

generates a code of length 22 over F4[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+27x^52+204x^55+330x^56+1056x^59+513x^60+3288x^63+1071x^64+4800x^67+1257x^68+2940x^71+714x^72+111x^76+60x^80+12x^84

The gray image is a linear code over GF(4) with n=88, k=7 and d=52.
This code was found by Heurico 1.16 in 0.364 seconds.