The generator matrix

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

generates a code of length 23 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+228x^54+144x^55+339x^56+1236x^57+1956x^58+1848x^59+2328x^60+4992x^61+8496x^62+6144x^63+6477x^64+13272x^65+25272x^66+17424x^67+13371x^68+24624x^69+39156x^70+21552x^71+14715x^72+19956x^73+21924x^74+8184x^75+3588x^76+3504x^77+1272x^78+72x^80+51x^84+12x^88+6x^92

The gray image is a linear code over GF(4) with n=92, k=9 and d=54.
This code was found by Heurico 1.16 in 59.2 seconds.