The generator matrix

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

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+90x^56+132x^59+525x^60+192x^61+384x^63+1470x^64+576x^65+936x^67+3726x^68+1344x^69+1056x^71+3726x^72+960x^73+564x^75+537x^76+99x^80+60x^84+6x^88

The gray image is a linear code over GF(4) with n=92, k=7 and d=56.
This code was found by Heurico 1.16 in 0.395 seconds.