The generator matrix

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

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+12x^51+357x^52+96x^54+180x^55+816x^56+192x^57+1152x^58+1080x^59+2064x^60+1728x^61+5184x^62+3240x^63+4422x^64+5184x^65+10368x^66+4860x^67+5064x^68+5184x^69+7776x^70+2916x^71+2919x^72+444x^76+186x^80+39x^84+9x^88

The gray image is a linear code over GF(4) with n=88, k=8 and d=48.
This code was found by Heurico 1.16 in 5.01 seconds.