The generator matrix

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

generates a code of length 30 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+267x^80+408x^81+384x^82+1293x^84+1380x^85+720x^86+1887x^88+1476x^89+912x^90+2205x^92+2028x^93+624x^94+1344x^96+852x^97+432x^98+147x^100+21x^104+3x^108

The gray image is a linear code over GF(4) with n=120, k=7 and d=80.
This code was found by Heurico 1.16 in 0.462 seconds.