The generator matrix

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

generates a code of length 29 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+504x^75+876x^76+564x^77+780x^78+2316x^79+2067x^80+2064x^81+1500x^82+4500x^83+3885x^84+3828x^85+3780x^86+7020x^87+5898x^88+4764x^89+3636x^90+6756x^91+4248x^92+2472x^93+1056x^94+1944x^95+918x^96+132x^97+9x^100+12x^104+6x^108

The gray image is a linear code over GF(4) with n=116, k=8 and d=75.
This code was found by Heurico 1.16 in 7.21 seconds.