The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+162x^52+264x^53+72x^54+288x^55+1056x^56+1008x^57+576x^58+1248x^59+2445x^60+3312x^61+1872x^62+4128x^63+5238x^64+7296x^65+3456x^66+6048x^67+6624x^68+7752x^69+3240x^70+3648x^71+3732x^72+1872x^73+117x^76+63x^80+12x^84+6x^88

The gray image is a linear code over GF(4) with n=88, k=8 and d=52.
This code was found by Heurico 1.16 in 4.87 seconds.