The generator matrix

 1  0  0  1  1  1  2  0  1  1  1  1  0  2  1  1  2  1  1  2  0  0  1  1  X  2  1  1 X+2  0  1  1 X+2  1  0  1  1 X+2  X  1  0  1  1 X+2  1  1  1 X+2  2  1  1 X+2  1 X+2 X+2  1  0  1  1  1  1  0  X  X X+2  1  2  1  1  X  0  1  1  1  X  1  2  1  1  1  1  X  0  1  1
 0  1  0  0  1  1  1  2  2  2  3  3  1  1  0  1  1  0  1  1  X  1  0  1  2  1  3  2  X  1  0  1  0  3  1 X+1  2 X+2  1 X+1  1  X  X  1  X X+1 X+2  2  1 X+3  3  1  X  1  2 X+2  1 X+1  1 X+2 X+1  X  1  1  1 X+3  1 X+2 X+1  1  1 X+2  0 X+2  1 X+2  1  3  2 X+3  3  0  0  0  1
 0  0  1  1  2  3  1  1  0  1  2  3  0  3  0  2  0 X+1 X+3 X+3  1  X  X X+2  1 X+1 X+3 X+1  1  X  X X+2  1 X+2  X X+1  X  1 X+1  1  X  3 X+3  3  3  0 X+2  1  3  X  3  X X+3 X+2  1  X  1  3 X+3 X+3  1  1  3 X+1  1  2 X+1 X+1 X+3  2 X+3  0  1  1  0  2  1  3  0 X+1  1  1  1  X  0
 0  0  0  X  0  X  X  X  X  0  X  0  X  0 X+2 X+2  2  X  X  0  0 X+2  2  2 X+2 X+2  2  2 X+2  X  0  0  2  X  2 X+2 X+2  2  0  2  0  X  0 X+2  2  0 X+2  X X+2 X+2 X+2  X  X  2  0  0  2  2 X+2  2  X X+2  X X+2  0  X  X X+2  2  2  2  0  2 X+2  X  X  2  2  2 X+2  X  0 X+2  X  X

generates a code of length 85 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+46x^79+131x^80+250x^81+279x^82+188x^83+204x^84+190x^85+136x^86+140x^87+103x^88+86x^89+54x^90+52x^91+34x^92+26x^93+56x^94+22x^95+16x^96+24x^97+3x^98+6x^100+1x^104

The gray image is a code over GF(2) with n=340, k=11 and d=158.
This code was found by Heurico 1.11 in 0.417 seconds.