The generator matrix

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

generates a code of length 23 over F4[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+192x^55+834x^56+648x^57+1680x^58+2544x^59+3588x^60+3372x^61+6408x^62+9408x^63+9855x^64+9600x^65+19776x^66+21408x^67+18378x^68+18984x^69+35184x^70+28416x^71+19314x^72+14808x^73+15984x^74+11760x^75+7272x^76+1740x^77+840x^78+84x^80+42x^84+24x^88

The gray image is a linear code over GF(4) with n=92, k=9 and d=55.
This code was found by Heurico 1.16 in 308 seconds.