The generator matrix

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

generates a code of length 22 over F4[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+63x^48+300x^52+384x^56+1332x^60+5229x^64+7656x^68+720x^72+468x^76+195x^80+36x^84

The gray image is a linear code over GF(4) with n=88, k=7 and d=48.
This code was found by Heurico 1.16 in 0.645 seconds.