The generator matrix 1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 a a+1 0 (a+1)X+1 (a+1)X+a+1 a 1 0 (a+1)X+1 (a+1)X+a+1 1 a 0 1 (a+1)X+a+1 (a+1)X+1 a 1 (a+1)X+a+1 X X aX+a+1 X+a+1 a+1 X+a (a+1)X+1 a+1 (a+1)X+a X+1 aX+1 0 0 0 (a+1)X 0 0 0 X aX X X X (a+1)X (a+1)X (a+1)X 0 0 aX (a+1)X (a+1)X (a+1)X 0 (a+1)X X aX X (a+1)X X X X aX 0 0 0 0 0 0 0 X 0 X (a+1)X (a+1)X X (a+1)X 0 (a+1)X X 0 aX X X aX (a+1)X (a+1)X (a+1)X 0 X X aX 0 (a+1)X (a+1)X 0 aX aX (a+1)X X aX 0 0 0 0 (a+1)X (a+1)X (a+1)X (a+1)X 0 aX X aX 0 aX 0 aX aX X 0 X X (a+1)X (a+1)X aX 0 X 0 aX (a+1)X X aX aX 0 (a+1)X generates a code of length 34 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 88. Homogenous weight enumerator: w(x)=1x^0+78x^88+96x^89+204x^91+324x^92+408x^93+744x^95+498x^96+912x^97+1320x^99+1098x^100+1920x^101+2208x^103+1218x^104+2064x^105+1452x^107+630x^108+744x^109+216x^111+126x^112+54x^116+48x^120+6x^124+15x^128 The gray image is a linear code over GF(4) with n=136, k=7 and d=88. This code was found by Heurico 1.16 in 0.68 seconds.