The generator matrix

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

generates a code of length 22 over F4[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+87x^52+72x^53+12x^54+384x^55+1197x^56+540x^57+144x^58+1776x^59+3171x^60+2304x^61+648x^62+5808x^63+7428x^64+5832x^65+1296x^66+8400x^67+9066x^68+5784x^69+972x^70+5136x^71+4470x^72+828x^73+99x^76+69x^80+9x^84+3x^88

The gray image is a linear code over GF(4) with n=88, k=8 and d=52.
This code was found by Heurico 1.16 in 4.68 seconds.