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

generates a code of length 23 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+300x^57+240x^58+576x^59+1080x^60+1644x^61+1104x^62+1884x^63+2817x^64+4500x^65+2928x^66+4428x^67+4983x^68+7524x^69+5232x^70+6228x^71+5964x^72+6384x^73+2784x^74+2244x^75+1509x^76+1152x^77+18x^80+9x^84+3x^92

The gray image is a linear code over GF(4) with n=92, k=8 and d=57.
This code was found by Heurico 1.16 in 4.68 seconds.