The generator matrix

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

generates a code of length 23 over F4[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+183x^56+108x^57+252x^58+1212x^59+798x^60+576x^61+1392x^62+2976x^63+2178x^64+1944x^65+3912x^66+8568x^67+4203x^68+3456x^69+6192x^70+10560x^71+4464x^72+2844x^73+3612x^74+4332x^75+1332x^76+288x^77+87x^80+51x^84+15x^88

The gray image is a linear code over GF(4) with n=92, k=8 and d=56.
This code was found by Heurico 1.16 in 5.05 seconds.