The generator matrix

 1  0  0  0  1  1  1  X  1 aX  1  1  1  1  X  1  1  1  1  1  1  1
 0  1  0  0  X  1 X+1  1 (a+1)X  1 (a+1)X+1 (a+1)X+a a+1  X  1 aX aX+a (a+1)X+a aX+a (a+1)X+a+1  X  1
 0  0  1  0 (a+1)X+1  1 (a+1)X (a+1)X+1 aX+1  a aX aX+a X+1 a+1  a  0 aX+1  a (a+1)X X+a+1 aX+a+1 X+a+1
 0  0  0  1 a+1  X aX+a+1 aX+a+1  a aX (a+1)X+a aX+1 X+1 (a+1)X+1 X+a+1 X+a a+1  X (a+1)X+a+1 (a+1)X+a (a+1)X aX+a

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

Homogenous weight enumerator: w(x)=1x^0+204x^54+240x^55+690x^56+1068x^57+1164x^58+1428x^59+2193x^60+2580x^61+3504x^62+3588x^63+5061x^64+4572x^65+6288x^66+6780x^67+7461x^68+5724x^69+5028x^70+3324x^71+2481x^72+1416x^73+708x^74+15x^76+12x^80+3x^84+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 4.29 seconds.