The generator matrix

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

generates a code of length 22 over F4[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+120x^51+201x^52+252x^53+912x^54+1668x^55+2859x^56+1788x^57+4020x^58+7764x^59+9300x^60+4872x^61+10944x^62+23832x^63+23433x^64+10152x^65+26472x^66+37392x^67+29766x^68+10428x^69+16464x^70+20964x^71+12108x^72+3228x^73+2628x^74+420x^75+84x^76+54x^80+9x^84+9x^88

The gray image is a linear code over GF(4) with n=88, k=9 and d=51.
This code was found by Heurico 1.16 in 56.9 seconds.