The generator matrix

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

generates a code of length 22 over F4[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+441x^60+252x^61+264x^62+216x^63+411x^64+468x^65+240x^66+48x^67+534x^68+324x^69+264x^70+120x^71+396x^72+108x^73+9x^76

The gray image is a linear code over GF(4) with n=88, k=6 and d=60.
This code was found by Heurico 1.16 in 0.031 seconds.