The generator matrix

 1  0  0  1  1  1 (a+1)X  1  1  1  1  1  1  1  1 (a+1)X  X  1  1  1  1  0  X
 0  1  0  1  a a+1  1 (a+1)X (a+1)X (a+1)X+1 (a+1)X+a+1  1 a+1 aX aX+1  1  1 aX+1 aX+a+1 X+a (a+1)X+1  1  1
 0  0  1 a+1  a  1 aX+1  1 a+1 aX aX X+1 aX+a+1 (a+1)X+a+1 aX+a aX (a+1)X+a aX+a (a+1)X+a aX+a+1 aX+a a+1 X+a+1
 0  0  0  X  0  X  0 (a+1)X aX (a+1)X aX (a+1)X aX (a+1)X  X  X (a+1)X aX  0  X  0  0  X

generates a code of length 23 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+531x^60+1008x^62+1620x^64+1776x^66+2682x^68+3024x^70+2898x^72+1872x^74+951x^76+9x^80+12x^84

The gray image is a linear code over GF(4) with n=92, k=7 and d=60.
This code was found by Heurico 1.16 in 0.264 seconds.