The generator matrix

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

generates a code of length 24 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+249x^60+480x^61+432x^62+1104x^63+1659x^64+1968x^65+1140x^66+2928x^67+3861x^68+4488x^69+2628x^70+6192x^71+6732x^72+6504x^73+3420x^74+6672x^75+5991x^76+4728x^77+1596x^78+1536x^79+936x^80+264x^81+27x^84

The gray image is a linear code over GF(4) with n=96, k=8 and d=60.
This code was found by Heurico 1.16 in 4.63 seconds.