The generator matrix

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

generates a code of length 15 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+696x^35+402x^36+648x^37+864x^38+2280x^39+2151x^40+2952x^41+2880x^42+6552x^43+6858x^44+7512x^45+7008x^46+9528x^47+6915x^48+4248x^49+1536x^50+2448x^51+30x^52+21x^56+6x^60

The gray image is a linear code over GF(4) with n=60, k=8 and d=35.
This code was found by Heurico 1.16 in 49.9 seconds.