The generator matrix

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

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+399x^52+492x^53+552x^54+1296x^55+2451x^56+3360x^57+3600x^58+5364x^59+10488x^60+9816x^61+10992x^62+15072x^63+24912x^64+20352x^65+21696x^66+25992x^67+33117x^68+21468x^69+17064x^70+13104x^71+12444x^72+5952x^73+1392x^74+612x^75+78x^76+45x^80+30x^84+3x^88

The gray image is a linear code over GF(4) with n=88, k=9 and d=52.
This code was found by Heurico 1.16 in 99.8 seconds.