The generator matrix

 1  0  0  0  1  1  1  X  1 a^2*X  1  1  X  1  1
 0  1  0  0  X  1 X+1  1 a*X  1 a^2*X+1 a^2  1 a^2*X+a^2 a^2*X
 0  0  1  0 a^2*X+1  1 a^2*X a^2*X+1 X+1 X+a a^2*X+a^2  a  X a^2*X a^2
 0  0  0  1 a^2  X a*X+a^2 a*X+a^2 a^2*X+a a^2*X  X  a X+a^2 a^2*X+a^2 a^2*X+a

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

Homogenous weight enumerator: w(x)=1x^0+528x^35+432x^36+696x^37+1044x^38+2400x^39+2190x^40+2808x^41+2436x^42+7200x^43+7827x^44+6120x^45+5436x^46+10848x^47+7413x^48+4200x^49+1836x^50+2064x^51+42x^52+12x^56+3x^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 17.3 seconds.