The generator matrix

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

generates a code of length 22 over F4[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+252x^54+252x^55+387x^56+1020x^57+1500x^58+1836x^59+1362x^60+3012x^61+3420x^62+4500x^63+2769x^64+6156x^65+7020x^66+7524x^67+4224x^68+6828x^69+5304x^70+4320x^71+1458x^72+1416x^73+936x^74+30x^76+6x^80+3x^88

The gray image is a linear code over GF(4) with n=88, k=8 and d=54.
This code was found by Heurico 1.16 in 4.33 seconds.