The generator matrix

 1  0  0  0  1  1  1  X  1 a^2*X  1  X  1  1  1
 0  1  0  0  X  1 X+1  1 a*X  1 X+a^2  1 a*X a*X+1 a^2
 0  0  1  0 a^2*X+1  1 a^2*X a^2*X+1 X+1 a^2*X+a  X X+a a^2*X+a a*X  1
 0  0  0  1 a^2  X a*X+a^2 a*X+a^2  a a^2*X a^2*X+a^2 a^2*X+a^2 a*X+a  0 a*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+588x^35+303x^36+1008x^37+576x^38+2784x^39+1422x^40+3888x^41+1152x^42+9432x^43+5148x^44+9168x^45+1728x^46+14208x^47+4833x^48+5904x^49+1152x^50+2172x^51+63x^52+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 72.3 seconds.