The generator matrix

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

generates a code of length 30 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+75x^88+96x^90+72x^92+9x^96+3x^104

The gray image is a linear code over GF(4) with n=120, k=4 and d=88.
This code was found by Heurico 1.16 in -3.24e-008 seconds.